Accurate three-dimensional printing

ABSTRACT

The present disclosure provides three-dimensional (3D) printing methods, apparatuses, and systems using, inter alia, a controller that regulates formation of at least one 3D object (e.g., in real time during the 3D printing); and a non-transitory computer-readable medium facilitating the same. For example, a controller that regulates a deformation of at least a portion of the 3D object. The control may be in situ control. The control may be real-time control during the 3D printing process. For example, the control may be during a physical-attribute pulse. The present disclosure provides various methods, apparatuses, systems and software for estimating the fundamental length scale of a melt pool, and for various tools that increase the accuracy of the 3D printing.

CROSS-REFERENCE

This application is a continuation application of U.S. application Ser.No. 15/435,110, filed Feb. 16, 2017, which claims priority to: U.S.Provisional Patent Application Ser. No. 62/297,067, filed on Feb. 18,2016, U.S. Provisional Patent Application Ser. No. 62/320,334, filed onApr. 8, 2016, U.S. Provisional Patent Application Ser. No. 62/325,402,filed on Apr. 20, 2016, U.S. Provisional Patent Application Ser. No.62/401,534, filed on Sep. 29, 2016, and U.S. Provisional PatentApplication Ser. No. 62/444,069, filed on Jan. 9, 2017, each of which isentirely incorporated herein by reference.

BACKGROUND

Three-dimensional (3D) printing (e.g., additive manufacturing) is aprocess for making three-dimensional (3D) objects of any shape from adesign. The design may be in the form of a data source such as anelectronic data source, or may be in the form of a hard copy. The hardcopy may be a two-dimensional representation of a 3D object. The datasource may be an electronic 3D model. 3D printing may be accomplishedthrough an additive process in which successive layers of material arelaid down one on top of each other. This process may be controlled(e.g., computer controlled, manually controlled, or both). A 3D printercan be an industrial robot.

3D printing can generate custom parts quickly and efficiently. A varietyof materials can be used in a 3D printing process including elementalmetal, metal alloy, ceramic, elemental carbon, resin, or polymericmaterial. In a typical additive 3D printing process, a firstmaterial-layer is formed, and thereafter, successive material-layers (orparts thereof) are added one by one, wherein each new material-layer isadded on a pre-formed material-layer, until the entire designedthree-dimensional structure (3D object) is materialized.

3D models may be created utilizing a computer aided design package orvia 3D scanner. The manual modeling process of preparing geometric datafor 3D computer graphics may be similar to plastic arts, such assculpting or animating. 3D scanning is a process of analyzing andcollecting digital data on the shape and appearance of a real object.Based on this data, 3D models of the scanned object can be produced. The3D models may include computer-aided design (CAD).

Many additive processes are currently available. They may differ in themanner layers are deposited to create the materialized structure. Theymay vary in the material or materials that are used to generate thedesigned structure. Some methods melt or soften material to produce thelayers. Examples for 3D printing methods include selective laser melting(SLM), selective laser sintering (SLS), direct metal laser sintering(DMLS), shape deposition manufacturing (SDM) or fused depositionmodeling (FDM). Other methods cure liquid materials using differenttechnologies such as stereo lithography (SLA). In the method oflaminated object manufacturing (LOM), thin layers (made inter alia ofpaper, polymer, metal) are cut to shape and joined together.

SUMMARY

At times, at least a portion of a layer within the printedthree-dimensional (abbreviated herein as “3D”) object may bend, warp,roll, curl, or otherwise deform during the 3D printing process. In someinstances, it is desired to control the way at least a portion of alayer of hardened material (e.g., 3D object) is formed. For example, attimes it is desired to control the deformation of at least a layerwithin the 3D object. The control may include control of the degreeand/or direction of the deformation. In some instances, it may bedesired to control the deformation of at least a surface of the 3Dobject. It may be desired to control the 3D object during its formation(e.g., in real time). At times, it may be desired to control theformation of the 3D object using open loop control, closed loop control,or any combination thereof. At times, it may be desired to control theformation of the 3D object using feed forward control, feed backcontrol, or any combination thereof The present disclosure delineatesdetection, control, or both detection and control, of at least the(e.g., afore-mentioned) deformations disclosed herein using at least oneof the (e.g., afore-mentioned) control methodologies disclosed herein.The present disclosure delineates reduction (e.g., attenuation and/orprevention) of at least the (e.g., afore-mentioned) degree and/ordirection of deformations disclosed herein, using various detectionand/or control methodologies.

In some embodiments, the present disclosure delineates methods, systems,apparatuses, and/or software that allow modeling of 3D objects with areduced amount of design constraints (e.g., no design constraints). Thepresent disclosure delineates methods, systems, apparatuses, andsoftware that allow materialization (e.g., printing) of these 3D objectmodels.

In an aspect described herein are methods, systems, apparatuses, and/orsoftware for generating a 3D object with a controlled degree ofdeformation. The controlled degree may comprise controlling the amountand/or direction of deformation. The controlled degree may comprisecontrolling the type of deformation. The deformation may comprise acurvature. The curvature may be a curvature of at least a portion of alayer within the 3D object.

In another aspect described herein are methods, systems, apparatuses,and/or software for generating a 3D object with a reduced degree ofdeformation (e.g., substantially non-deformed). The 3D object can bedevoid of auxiliary support (e.g., devoid of one or more auxiliarysupports), or comprise of one or more auxiliary supports. The 3D objectcan be devoid of a mark indicating the prior presence of auxiliarysupport (e.g., one or more auxiliary supports).

In another aspect described herein are methods, systems, apparatuses,and/or software for generating a 3D object with a smooth (e.g.,polished, continuous, or regular) and/or planar (e.g., non-warped)bottom surface.

In another aspect, a method for generating a multi layered object from adesired model comprises: transforming at least a portion of a powder bedwith an energy beam to form a portion of the multi layered object,measuring a measured curvature deformation in the multi layered object,and controlling the measured curvature deformation of the multi layeredobject to achieve a target deformation curvature by altering at leastone parameter of the transforming, wherein the measuring and thecontrolling occurs during the transforming of the portion of the layerof the powder bed, and wherein the multi layered object substantiallycorresponds to the desired model.

The curvature may comprise a warpage. The curvature may comprise adeviation of at least a portion of the multi layered object in alocation away from the energy beam. Away may be away from the positionat which the energy beam interacts with the powder bed. Away may be atleast about 2 millimeters. The controlling may comprise controlling theenergy beam. The measured deformation curvature may comprise adeformation in the vertical direction. The measured deformationcurvature may comprise a deformation in the horizontal direction. Thetarget deformation curvature may be substantially zero. The targetdeformation curvature may be positive. The target deformation curvaturemay be substantially zero. The target deformation curvature may benegative. The method may further comprise a deformed model, wherein thedeformed model comprises one or more deformation of the desired model.The multi layered object may be generated according to the deformedmodel. The generated multi layered object may substantially correspondto the desired model. The deformed model may be generated such that thegeneration of the multi layered object comprising the target deformationcurvature will incorporate a corrective deformation. The targetdeformation may comprise the corrective deformation. The targetdeformation may substantially correspond to the corrective deformation.The target deformation may substantially correspond to a modeling of ahardening and/or cooling of a transformed material having a shape of thecorrective deformation. The deformed model may be generated such thatthe generation of the multi layered object with the target deformationcurvature will substantially result in the multi layered object (e.g.,upon hardening and/or cooling) such that the multi layered objectsubstantially corresponds to the desired model (e.g., upon coolingand/or hardening). The desired model may be a model of a desired 3Dobject. The curvature deformation may be a curvature that materialized(e.g., came about) due to deformation of a transformed material (e.g.,upon cooling and/or hardening of the transformed material). Thehardening may be solidifying. The transforming may be melting. Thecontrolling operation may comprise controlling the at least a portionsuch that it will substantially correspond to the target deformation.The target deformation may correspond to a modeling of the at least aportion that is hardened.

In another aspect, a method for generating a multi layered objectcomprises: dispensing a first layer of powder material to form a powderbed; transforming at least a portion of the first layer of powdermaterial with an energy beam to form a first transformed materialportion; dispensing a second layer of powder material adjacent to thefirst layer of powder material; transforming at least a portion of thesecond layer of powder material with the energy beam to form a secondtransformed material portion, wherein at least a fraction of the secondtransformed material portion is connected to the first transformedmaterial portion to form at least a portion of the multi layered object;and deforming the multi layered object to comprise a curvature, whichcurvature is measured and controlled during the transforming of the atleast a portion of the second layer of powder material.

The curvature can be positive or negative. The multi layered object mayprotrude from the exposed surface of the powder bed. The measured maycomprise measuring at least a portion of a protrusion of the multilayered object that protrudes from the material bed. The measured maycomprise measuring a height of the powder bed. The measured may comprisemeasuring a height of one or more positions at the exposed surface ofthe powder bed. The measured may comprise measuring a transformedmaterial portion in the powder bed. The measured may comprise measuringa transformed material portion in the powder bed. The transformedmaterial portion may comprise the first transformed material portion orthe second transformed material portion. The measured may comprisemeasuring a height of an area having a radius of at least 5 mm around alocation of the transforming. The controlled may comprise controlling apower of an energy source producing the energy beam. The controlled maycomprise measuring a temperature of a location of the transforming. Thecontrolled may comprise controlling the power of the energy source whilemeasuring the temperature of a location of the transforming. Thecontrolled may comprise controlling a power density of the energy beamwhile measuring the temperature of a location of the transforming. Thecontrolled may comprise controlling the energy per unit area of theenergy beam. Controlled may comprise controlling the energy per unitarea of the energy beam while measuring the temperature of a location ofthe transforming. Transforming may comprise fusing. Fusing may comprisemelting. Controlled may comprise controlling a size of a molten area onthe surface of the second layer of powder material. Controlled maycomprise controlling a size of the second transformed material portion.Dispensing may comprise using a layer dispensing mechanism comprising acyclonic separator.

In another aspect, a system for forming a multi layered objectcomprises: a powder dispenser that is configured to dispense a firstlayer of powder material to form a powder bed; an energy source that isconfigured to generate an energy beam, which energy beam is configuredto transform (e.g., is capable of transforming) at least a portion ofthe powder bed to form a first transformed material portion as part ofthe multi layered object; and at least one controller operativelycoupled to the powder dispenser, and energy source, and is programmedto: (i) direct the powder dispenser to dispense a first layer of powdermaterial to form a powder bed; (ii) direct the energy beam to transformat least a portion of the first layer of powder material to form a firsttransformed material portion; (iii) direct the powder dispenser todispense a second layer of powder material adjacent to the first layerof powder material; (iv) direct the energy beam to transform at least aportion of the second layer of powder material to form a secondtransformed material portion, wherein at least a fraction of the secondtransformed material portion is connected to the first transformedmaterial portion to form at least a portion of the multi layered object,and (v) direct the energy beam to deform the multi layered object tocomprise a curvature, which curvature is measured and controlled duringthe transforming at least a portion of the second layer of powdermaterial. The at least one controller may comprise a plurality ofcontrollers. At least two of operations (i) to (v) may be directed bythe same controller. At least two of operations (i) to (v) may bedirected by different controllers.

In another aspect, an apparatus for forming a multi layered object froma desired (e.g., requested) model comprises at least one controller thatis programmed to: (a) direct a powder dispenser to dispense a firstlayer of powder material to form a powder bed; (b) direct an energy beamto transform at least a portion of the first layer of powder material toform a first transformed material portion; (c) direct the powderdispenser to dispense a second layer of powder material adjacent to thefirst layer of powder material; (d) direct the energy beam to transformat least a portion of the second layer of powder material to form asecond transformed material portion, wherein at least a fraction of thesecond transformed material portion is connected to the firsttransformed material portion to form at least a portion of the multilayered object; and (e) direct deforming the multi layered object tocomprise a curvature, which curvature is measured and controlled duringthe transforming at least a portion of the second layer of powdermaterial, wherein the controller is operatively coupled to the energybeam, and powder dispenser. The direct deforming in operation (e) may beeffectuated by using the energy beam. The at least one controller maycomprise a plurality of controllers. At least two of operations (a) to(e) may be directed by the same controller. At least two of operations(a) to (e) may be directed by different controllers.

In another aspect, a method for generating a multi layered object from adesired model comprises: transforming at least a portion of a powder bedwith an energy beam to form at least a portion of the multi layeredobject, measuring a (e.g., curvature) deformation in the at least aportion of the multi layered object, and controlling the (e.g.,curvature) deformation of the at least a portion of the multi layeredobject to achieve a target deformation curvature by altering at leastone parameter of the transforming, wherein the measuring and thecontrolling occurs during the transforming of the portion of the powderbed, and wherein the multi layered object substantially corresponds tothe desired model.

Measuring the deformation and controlling the deformation may occurduring formation of one or more melt pools as part of the transforming.The curvature may comprise a warpage. The curvature may comprise adeviation of the at least a portion of the multi layered object withrespect to the requested model, which deviation is in a location awayfrom the energy beam. Away may be at least 2 millimeters. Away may beaway from the position at which the energy beam interacts with thepowder bed. Controlling may comprise controlling the energy beam. Thedeformation curvature may comprise a deformation in the verticaldirection. The deformation curvature may comprise a deformation in thehorizontal direction. The target deformation curvature may be (e.g.,substantially) zero. The target deformation curvature may be positive.Substantially may be relative to the intended purpose of the multilayered (e.g., 3D) object. The method may further comprise a deformedmodel. The deformed model may comprise the desired model that underwentat least one deviation, wherein the multi layered object is generatedaccording to the deformed model, and wherein the generated multi layeredobject (e.g., substantially) corresponds to the desired model. Thedeformed model may be generated such that the generation of the multilayered object with the target deformation curvature will (e.g.,substantially) result in the desired model. Controlling may comprisecontrolling the at least a portion of the multi layered object such thatit will (e.g., substantially) correspond to the target deformation. Thetarget deformation may correspond to a modeling of the at least aportion of the multi layered object (e.g., that is hardened). Hardenedmay comprise solidified.

In another aspect, a system for forming a multi layered object from adesired model comprises: (e.g., an enclosure configured to contain) apowder bed; an energy source that is configured to generate an energybeam, which energy beam is configured to transform at least a portion ofthe powder bed to form a transformed material as part of the multilayered object; a detector that is configured to detect a (e.g.,curvature) deformation in the multi layered object; and a controlleroperatively coupled to the powder bed, energy source, and to thedetector, which controller is programmed to: (i) direct the energy beamto transform at least a portion of the powder bed to form thetransformed material as at least a portion of the multi layered object;(ii) direct the detector to detect the (e.g., curvature) deformation;(iii) evaluate the degree of (e.g., curvature) deformation and produce aresult; and (iv) use the result to control the (e.g., curvature)deformation of the multi layered object to achieve a target deformation(e.g., curvature) by altering at least one parameter of the transform in(i), wherein the detect in (ii) and the control in (iv) occurs duringthe transform in (i), and wherein the multi layered object (e.g.,substantially) corresponds to the desired model. The detector may becalibrated (e.g., in situ) using a stationary position adjacent to thepowder bed. Measuring the deformation and controlling the deformationmay occur during formation of one or more melt pools as part of thetransforming. The energy source, detector, and/or controller may beoperatively coupled to the powder bed.

In another aspect, an apparatus for forming a multi layered object froma desired model comprises: at least one controller that is programmed to(a) direct an energy beam to transform at least a portion of a powderbed to form a transformed material, which transformed material forms atleast a portion of the multi layered object; (b) direct the detector todetect a (e.g., curvature) deformation in the at least a portion of themulti layered object; (c) evaluate the degree of (e.g., curvature)deformation to produce a result; and (d) use the result to control the(e.g., curvature) deformation of the multi layered object to achieve atarget deformation (e.g., curvature) by altering at least one parameterof the transform in (i), wherein the detect in (ii) and the control in(iv) occurs during the transform in (i), and wherein the multi layeredobject (e.g., substantially) corresponds to the desired model, whereinthe controller is operatively coupled to the energy beam, and detector.The control may be closed loop control. Substantially may be relative tothe intended purpose of the multi layered object. The at least onecontroller may comprise a plurality of controllers. At least two ofoperations (a) to (d) may be directed by the same controller. At leasttwo of operations (a) to (d) may be directed by different controllers.Measuring the deformation and controlling the deformation may occurduring formation of one or more melt pools as part of the transforming.

In another aspect, a computer software product for forming a multilayered object from a desired model, which computer software productcomprises a non-transitory computer-readable medium in which programinstructions are stored, which instructions, when read by a computer,cause the computer to perform operations comprising: (a) receive aninput signal from a sensor that measures a (e.g., curvature) deformationof at least a portion of the multi layered object during its formationfrom at least a portion of a powder bed by projecting an energy beam tothe powder bed, wherein the non-transitory computer-readable medium isoperatively coupled to the sensor; (b) direct controlling the (e.g.,curvature) deformation of the at least a portion of the multi layeredobject to achieve a target deformation curvature by altering at leastone parameter of the formation, wherein the receive an input signal in(a) and the direct controlling in (b) occur during the formation, andwherein the multi layered object substantially corresponds to thedesired model.

Altering at least one parameter of the formation may comprise alteringat least one characteristic of an energy beam based on a comparison ofthe input signal with a desired (e.g., curvature) deformation, whereinthe non-transitory computer-readable medium is operatively coupled tothe energy beam. The direct in (b) may be during the forming. Thecomputer software product may comprise sub-computer software products(e.g., modules). At least two of instructions relating to (a) to (b) maybe carried out by the same sub-computer software product. At least twoof instructions relating to (a) to (b) may be carried out by differentsub-computer software products. Measuring the deformation andcontrolling the deformation may occur during formation of one or moremelt pools as part of the transforming.

In another aspect, a method for printing a 3D object comprisingdisposing a pre-transformed material towards a platform (e.g., in anenclosure to form a material bed); transforming the pre-transformedmaterial (e.g., which constitutes at least a portion of the materialbed) with an energy beam to form a transformed material portion as partof the 3D object, which transforming over time yields a plurality ofphysical-attribute pulses, wherein the transformed material portioncomprises a plurality of melt pools that correspond to the plurality ofphysical-attribute pulses; and controlling at least a portion of aphysical-attribute pulse within the plurality of physical-attributepulses in real time during the transforming.

Controlling may comprise controlling one or more mechanism of the 3Dprinter and/or components of the 3D printing to affect the at least aportion of the phenomenon pulse. Controlling may comprise controllingthe process of detecting the phenomenon. At least two of the pluralityof physical-attribute pulses may be (e.g., controllably and/orpurposefully) different. The physical-attribute may comprise adetectable energy. The detectable energy may be an irradiated energy.The transformed material portion may comprise a plurality of melt poolsthat correspond to the plurality of measureable energy pulses. Thephysical-attribute can correspond to a temperature of the plurality ofmelt pools, temperature adjacent to the plurality of melt pools, powerof an energy source that generates the energy beam, power density of theenergy beam, or any combination thereof. The physical attribute canrelate to a temperature comprising a temperature of the melt pool, or atemperature of an area adjacent to the melt pool. The method may furthercomprise measuring an intensity and/or wavelength of a radiation. Themethod may further comprise correlating the intensity and/or wavelengthof the radiation to a temperature. The radiation may be from the meltpool, or from an area adjacent to the melt pool. The radiation may befrom a footprint of the energy beam on the at least a portion, or froman area adjacent to the footprint of the energy beam on the at least aportion. The method may further comprise detecting the plurality ofphysical-attribute pulses by detecting one or more wavelengthsirradiated (e.g., emitted) from the at least a portion. The method mayfurther comprise detecting a radiation characteristics comprisingwavelength or intensity, which radiation is emitted from the melt pool,from an area adjacent to the melt pool, or from any combination thereof.The method may further comprise detecting a radiation characteristicscomprising wavelength or intensity, which radiation is emitted from afootprint of the energy beam on the at least a portion, from an areaadjacent to the footprint of the energy beam on the at least a portion,or from any combination thereof The method may further comprisecorrelating the intensity of the radiation, wavelength of the radiation,or both the intensity and wavelength of the radiation to a temperaturevalue. Adjacent to the melt pool can be at a distance of at most abouttwo, three, four, five, or six melt pool diameters from thecircumference of the melt pool. The plurality of melt pools may have asubstantially identical respective fundamental length scale. Real timecan comprise during formation of one or more of the plurality of meltpools. Real time can comprise during formation of two of the pluralityof melt pools. Real time can comprise during formation of one of theplurality of melt pools. The method may further comprise detecting thephysical-attribute pulse with a detector. The detector can comprise asingle pixel detector. The detector can comprise an image detector. Thedetector can comprise an optical measurement. The detector can comprisean optical fiber. The detector can comprise an optical position sensor.The detector can comprise a photo detector. The detector can comprise aphotodiode. The physical-attribute may correspond to the temperature ofthe material bed (e.g., exposed surface thereof), power of the energysource, or power density of the energy beam. The measurable (e.g.,detectable) energy may be the temperature of the material bed (e.g.,exposed surface thereof), power of the energy source, or power densityof the energy beam. The temperature of the material bed may be along thetrajectory of the energy beam on the exposed surface of the materialbed. Real time may be during at least a portion of the 3D printing. Realtime may be during formation of a layer of the 3D object. Real time maybe during formaiton of a hatch line. Real time may be during formationof two melt pools as part of the 3D object. Real time may be duringformaiton of a melt pool as part of the 3D object. The pre-transformedmaterial may be a powder material. The pre-transformed material can beat least a portion of a material bed. The material bed can be planarizedduring the printing using a layer dispensing mechanism comprising acyclonic separator. The material bed may be a powder bed. Thepre-transformed material may be selected from at least one member of thegroup consisting of metal alloy, elemental metal, ceramic, and anallotrope of elemental carbon. Dispensing may comprise using a layerdispensing mechanism. The layer dispensing mechanism may comprise acyclonic separator. The transformed material portion may comprise atleast one melt pool, and wherein the physical-attribute may comprisemelt pool temperature, fundamental length scale (FLS), or reflectivity.The fundamental length scale (FLS) may comprise height, depth, ordiameter (e.g., or diameter equivalence). The physical-attribute pulsemay comprise a dwell time and an intermission. The dwell time maycomprise a leading edge and/or a tailing edge. The method may furthercomprise using the controlling to maintain (e.g., over time) asubstantially identical leading edge, or tailing edge of the pluralityof physical-attribute pulses over time. The method may further comprisemaintaining over time a substantially identical leading-edge, tailingedge, plateau, or any combination thereof (e.g., by using thecontrolling). The dwell time may comprise a plateau. The method mayfurther comprise maintaining a substantially identical plateau of theplurality of physical-attribute pulses over time (e.g., by using thecontrolling). Identical may comprise identical in terms of intensity,time span, or any combination thereof. Controlling may comprise closeloop control. The close loop control may comprise a loop sample time ofat most about 20 milliseconds. Controlling may comprise calculating.Calculating can be performed during the dwell time (e.g., of the energybeam). The calculating can be performed during the intermission (e.g.,of the energy beam). The calculating may not be performed during thedwell time. The calculating may not be performed during theintermission. The calculating may occur during at most about 20microseconds. The method may further comprise maintaining asubstantially identical profile of the plurality of physical-attributepulses over time (e.g., by using the controlling). The profile maycomprise an energy profile of the energy beam. The profile may comprisea temperature profile of the portion of the material bed (e.g., alongthe trajectory of the energy beam) over time. The profile may comprise apower density profile of the energy beam over time. The energy profilemay comprise a power profile of the energy source over time. Thetransformed material portion may comprise at least one melt pool. Theprofile may comprise a temperature of the melt pool. The transformedmaterial portion may comprise at least one melt pool. The profile maycomprise a fundamental length scale (e.g., depth, diameter, or diameterequivalent) of the melt pool. The profile can comprise (i) a temperatureprofile of the plurality of melt pools, or (ii) a temperature profile ofa position adjacent to the plurality melt pools. Adjacent may be at adistance from a circumference of the melt pool, which distance is of atmost about six diameters of a melt pool generated by the energy beam,which melt pool is of the plurality of melt pools. The profile cancomprise a power density profile of the energy beam. The profile cancomprise a power profile of an energy source generating the energy beam.The controlling may comprise using a processor. The processor maycomprise parallel processing. The processor may comprise amicroprocessor, a data processor, a central processing unit (CPU), agraphical processing unit (GPU), a system-on-chip (SOC), a co-processor,a network processor, an application specific integrated circuit (ASIC),an application specific instruction-set processor (ASIPs), a controller,a programmable logic device (PLD), a chipset, or a field programmablegate array (FPGA). The processor may comprise a graphical processingunit (GPU). The processor may comprise a field programmable gate array(FPGA). The processor may comprise a multiplicity of processing units ina single physical processing unit. The multiplicity of processing unitsmay be parallel processing units. The multiplicity of parallelprocessing units can comprise at least about 200 parallel processingunits. The multiplicity of parallel processing units can comprise a coreor a digital signal processing slice. The multiplicity of parallelprocessing units may comprise a first processing unit and a secondprocessing unit, wherein the processor may comprise low latency in datatransfer from the first processing unit to the second processing unit.Latency is sufficiently low to allow a number of floating pointoperations per second (FLOPS) of at least about 10 Tera FLOPS. Latencyis sufficiently low to allow a number of multiply-accumulate operationsper second (MACs) of at least about 10 Tera MACs.

In another aspect, a system for forming a 3D object comprises: anenclosure configured to contain material bed; an energy source that isconfigured to generate an energy beam, which energy beam is configuredto transform at least a portion of the material bed to form atransformed material as part of the 3D object, which transform over timeforms a pulsing physical-attribute comprising a plurality ofphysical-attribute pulses (e.g., plurality of detectable energy pulses),which energy source is operatively coupled to the material bed; adetector that is configured to detect the physical-attribute, whichdetector is operatively coupled to the material bed; and at least onecontroller operatively coupled to the material bed, energy source, anddetector and is programmed to: (i) direct the energy beam to generatethe 3D object from at least a portion of the material bed; (ii)evaluates (e.g., or directs evaluation of) the physical-attributedetected by the detector; and (iii) using the evaluation to alter atleast one characteristic of the energy beam to form the 3D object. Theenergy source may be operatively coupled to the material bed.

Alter may comprise maintain a substantially identical physical-attributepulses within the multiplicity of pulses. The detector may be calibratedusing at least one stationary position adjacent to the material bed(e.g., to the exposed surface thereof). The transformed material portionmay comprise a plurality of melt pools that correspond to the pluralityof physical-attribute pulses. The at least one controller may comprise aplurality of controllers. At least two of operations (i) to (iii) may becontrolled by the same controller. At least two of operations (i) to(iii) may be controlled by different controllers. The physical-attributemay correspond to or comprise temperature of the material bed (e.g.,exposed surface thereof), power of the energy source, or power densityof the energy beam. The temperature of the material bed may be along thetrajectory of the energy beam on the exposed surface of the materialbed. The physical-attribute pulses may comprise a variation intemperature, energy source power, or energy beam power density, overtime. The physical-attribute may correspond to a (I) temperature of theplurality of melt pools, (II) temperature adjacent to the plurality ofmelt pools, (III) power of an energy source that generates the energybeam, (IV) power density of the energy beam, or (V) any combinationthereof. Adjacent to the melt pool can be at a distance of at most aboutsix melt pool diameters from the circumference of the melt pool. Altercan comprise maintain a (e.g., substantially) identicalphysical-attribute pulses within the multiplicity of pulses. Thedetected physical-attribute (e.g., comprising a detectable energy, or ameasurable energy) can comprise one or more wavelengths that are emittedfrom the at least a portion. The detected physical-attribute cancomprise a wavelength of a radiation or an intensity of the radiation,which radiation is emitted (I) from an area occupied by the footprint ofthe energy beam on the at least a portion, (II) from an area adjacent tothe area occupied by the footprint of the energy beam on the at least aportion, or (III) from any combination thereof The detectedphysical-attribute may comprise wavelength or intensity, which radiationis emitted (I) from the melt pool, (II) from an area adjacent to themelt pool, or (III) from any combination thereof The detector mayfurther correlate, or directs correlation of, (A) the intensity of theradiation, (B) wavelength of the radiation, or (C) both the intensityand wavelength of the radiation, to a temperature value. The controllingcan comprise using a processor. The processor can comprise amicroprocessor, a data processor, a central processing unit (CPU), agraphical processing unit (GPU), a system-on-chip (SOC), a co-processor,a network processor, an application specific integrated circuit (ASIC),an application specific instruction-set processor (ASIPs), a controller,a programmable logic device (PLD), a chipset, or a field programmablegate array (FPGA). The processor comprises a multiplicity of processingunits in a single physical processing unit that are parallel processingunits. The multiplicity of parallel processing units can comprise atleast about 200 parallel processing units. The multiplicity of parallelprocessing units can comprise a first processing unit and a secondprocessing unit, wherein the processor comprises low latency in datatransfer from the first processing unit to the second processing unit.Latency may be sufficiently low to allow a number of floating pointoperations per second (FLOPS) of at least about 10 Tera FLOPS.

In another aspect, a system for printing a 3D object comprising: anenclosure configured to contain a platform; an energy source that isconfigured to generate an energy beam that transforms thepre-transformed material to a transformed material as part of the 3Dobject, which transforms over time yields a plurality ofphysical-attribute pulses, wherein the transformed material comprises aplurality of melt pools that correspond to the plurality ofphysical-attribute pulses, which the energy source is operativelycoupled to the platform; a detector that is configured to detect theplurality of physical-attribute pulses, which detector is operativelycoupled to the platform; and at least one controller operatively coupledto the platform, energy source, and detector and is programmed to: (i)direct the energy beam to transform the pre-transformed material into atransformed material as a first portion of the 3D object; (ii) evaluate,or directs evaluation of, the plurality of physical-attribute pulses bythe detector; and (iii) use the evaluate to alter at least onecharacteristic of the energy beam to print a second portion of the 3Dobject.

The physical attribute may comprise a detectable and/or measureableenergy. The physical-attribute may correspond to a (I) temperature ofthe plurality of melt pools, (II) temperature adjacent to the pluralityof melt pools, (III) power of an energy source that generates the energybeam, (IV) power density of the energy beam, or (V) any combinationthereof. Adjacent to the melt pool can be at a distance of at most aboutsix melt pool diameters from the center of the melt pool. Alter cancomprise maintain a substantially identical physical-attribute pulseswithin the multiplicity of pulses. The physical-attribute can compriseone or more wavelengths that are emitted from the at least a portion.The physical-attribute can comprise a wavelength of a radiation or anintensity of the radiation, which radiation is emitted (I) from afootprint of the energy beam on the at least a portion, (II) from anarea adjacent to the footprint of the energy beam on the at least aportion, or (III) from any combination thereof. The physical-attributecan comprise wavelength or intensity, which radiation is emitted (I)from the melt pool, (II) from an area adjacent to the melt pool, or(III) from any combination thereof The detector may further correspondto, or directs a correlation of (A) the intensity of the radiation, (B)wavelength of the radiation, or (C) both the intensity and wavelength ofthe radiation, to a temperature value. The at least two of (i) to (iii)may be controlled by the same controller. The at least two of (i) to(iii) may be controlled by different controllers. The controlling cancomprise using a processor. The processor can comprise a microprocessor,a data processor, a central processing unit (CPU), a graphicalprocessing unit (GPU), a system-on-chip (SOC), a co-processor, a networkprocessor, an application specific integrated circuit (ASIC), anapplication specific instruction-set processor (ASIPs), a controller, aprogrammable logic device (PLD), a chipset, or a field programmable gatearray (FPGA). The processor can comprise a multiplicity of processingunits in a single physical processing unit that are parallel processingunits. The multiplicity of parallel processing units can comprise atleast about 200 parallel processing units. The multiplicity of parallelprocessing units can comprise a first processing unit and a secondprocessing unit, wherein the processor comprises low latency in datatransfer from the first processing unit to the second processing unit.Latency can be sufficiently low to allow a number of floating pointoperations per second (FLOPS) of at least about 10 Tera FLOPS. Thesystem may further comprise a layer dispensing mechanism that includes acyclonic separator, which layer dispensing mechanism is configured toplanarize a material bed disposed adjacent to the platform, whichmaterial bed comprises the pre-transformed material.

In another aspect, an apparatus for forming a 3D object comprises atleast one controller that is programmed to (a) direct an energy beam togenerate a transformed material from a pre-transformed material (e.g.,that is at least a portion of a material bed), which transformedmaterial forms at least a portion of the 3D object, which generate thetransformed material over time forms a plurality of physical-attributepulses; (c) direct a detector to detect the physical-attribute; and (d)control at least a portion within a physical-attribute pulse of theplurality of physical-attribute pulses, which control is during (a) andtakes into account the detect in (c), and wherein the at least onecontroller is operatively coupled to the detector, and to the energybeam.

The control can be closed loop control. The at least one controller maydirect an alteration in at least one characteristic of the energy beamaccording to the detect in (c). The transformed material portion cancomprise a plurality of melt pools that relate to the plurality ofphysical-attribute pulses. The at least one controller may comprise aplurality of controllers. At least two of operations (a) to (d) may becontrolled by the same controller. At least two of operations (a) to (d)may be controlled by different controllers. The physical-attribute maycomprise temperature of the material bed (e.g., exposed surfacethereof), power of the energy source, or power density of the energybeam. The temperature of the material bed may be along the trajectory ofthe energy beam on the exposed surface of the material bed. Thephysical-attribute pulses may comprise a variation in temperature,energy source power, or energy beam power density, over time.

In another aspect, a computer software product for forming at least one3D object, comprises a non-transitory computer-readable medium in whichprogram instructions are stored, which instructions, when read by acomputer, cause the computer to perform operations comprising: (a)receive an input signal from a sensor that comprises a pulsingphysical-attribute that arises during the formation of the 3D objectfrom a pre-transformed material (e.g., that is at least a portion of amaterial bed) by projecting an energy beam to the material bed, whereinthe non-transitory computer-readable medium is operatively coupled tothe sensor; (b) direct controlling at least a portion of aphysical-attribute pulse within the plurality of physical-attributepulses in real time during the formation of the 3D object.

Direct controlling may comprise altering at least one characteristic ofthe energy beam based on a comparison of the input signal with aphysical-attribute setpoint, wherein the non-transitorycomputer-readable medium is operatively coupled to the energy beam.Direct may be during the physical-attribute pulse. The transformedmaterial portion comprises a plurality of melt pools that relate to theplurality of physical-attribute pulses. The physical-attribute maycomprise temperature of the material bed (e.g., exposed surfacethereof), power of the energy source, or power density of the energybeam. The temperature of the material bed may be along the trajectory ofthe energy beam on the exposed surface of the material bed. Thephysical-attribute pulses may comprise a variation in temperature,energy source power, or energy beam power density, over time.

In another aspect, a method for printing a 3D object comprises: (a)disposing a pre-transformed material towards a platform; (b)transforming the pre-transformed material with an energy beam to form afirst melt pool as part of the 3D object, which first melt pool isdisposed on a target surface (e.g., that is disposed at or above theplatform); (c) detecting a physical attribute of the first melt pool toobtain a first physical attribute value during the printing; (d)detecting the physical attribute of a vicinity of the first melt pool toobtain a second physical attribute value during the printing; and (e)controlling the energy beam using the first physical attribute value,the second physical attribute value, or the first physical attributevalue and the second physical attribute value, which controlling isduring the printing.

Controlling the energy beam may be by using the first physical attributevalue and the second physical attribute value. The physical attributevalue can be correlated to the temperature. The physical attribute valuecan comprise an amplitude, or a wavelength of an electromagnetic beamthat irradiates from the target surface. The electromagnetic beam cancomprise an infra-red beam. The physical attribute value can comprise anamplitude, or a wavelength of an electromagnetic beam that is reflectedfrom the target surface. The detecting (e.g., in operations (c) and/or(d)) can comprise using an optical fiber that is coupled to a detector.The detecting in operation (c) can comprise using a first detector. Thedetecting in operation (d) can comprise using a second detector. Thefirst detector can be different from the second detector. The detectingin operation (c) can comprise using a first detector, and wherein thedetecting in operation (d) can comprise using a second detector set,wherein the first detector is different from the second detector set.The second detector set can comprise an optical fiber bundle comprisinga plurality of optical fibers. The plurality of optical fibers can beoperatively coupled to a plurality of detectors (e.g., respectively).The detecting in operation (d) can comprise averaging the signaldetected from the second detector set to obtain the second physicalattribute value. During the printing can comprise during formation of alayer, a plurality of melt pools within a layer, the first melt pool, orany combination threof The layer can be a portion of the 3D object.Controlling can comprise altering at least one characteristic of theenergy beam. At least one characteristic of the energy beam can comprise(i) the power density, (ii) the cross-section beam, (iii) the dwelltime, or (iv) the focus. Controlling can comprise comparing the firstphysical attribute value with the second physical attribute value.Controlling can comprise comparing (i) the first physical attributevalue with a respective first physical attribute threshold value, (ii)the second physical attribute value with a respective second physicalattribute threshold value, or (iii) the first physical attribute valuewith the second physical attribute threshold value. The printing cancomprise using a printing instruction to control the energy beam, andwherein the method further can comprise altering the printinginstruction using the comparing. Altering can be during the printing.Altering can be during the transforming to form the first melt pool. Thepre-transformed material can be at least a portion of a material bed,and wherein the material bed is planarized during the printing using alayer dispensing mechanism comprising a cyclonic separator. The vicinitycan be an area having a radius of at most about six fundamental lengthscales (e.g., diameters) of the first melt pool, that is concentric withthe first melt pool. The first melt pool can be substantially isotropic,homogenous, or isotropic and homogenous. Isotropic may be in terms ofshape, cross section (e.g., vertical and/or horizontal), aspect ratio(e.g. retaining substantially the same radius in the horizontal andvertical cross section), material property (e.g., microstructures), orany combination thereof. Homogenous may be in terms of material property(e.g., microstructures. The method may further comprise repeating atleast operation (b) to form a second melt pool. The first melt pool andthe second melt pool may be (e.g., substantially) identical in theirshape, cross section (e.g., horizontal and/or vertical), fundamentallength scale, material property (e.g., microstructures), or anycombination thereof.

In another aspect, a system for printing a 3D object comprises: anenclosure configured to contain a platform; an energy source that isconfigured to generate an energy beam that transforms a pre-transformedmaterial into a transformed material comprising a melt pool, which meltpool is a part of the 3D object, wherein the energy source isoperatively coupled to the platform; a first detector that is configuredto detect a physical-attribute of the melt pool, which detector isoperatively coupled to the platform; a second detector that isconfigured to detect the physical-attribute of a vicinity of the meltpool, which second detector is operatively coupled to the platform; andat least one controller operatively coupled to the platform, energysource, and detector and is programmed to: (i) direct the energy beam totransform the pre-transformed material to form a melt pool as part ofthe 3D object; (ii) direct detecting the physical-attribute of the meltpool by the first detector to obtain a first physical-attribute value;(iii) direct detecting the physical-attribute of the melt pool vicinityby the second detector to obtain a second physical-attribute value and(iv) use, or direct use of, the first physical-attribute value, secondphysical-attribute value, or the first physical-attribute value and thesecond physical-attribute value, to alter at least one characteristic ofthe energy beam during the printing.

The vicinity can be an area having a radius of at most about sixfundamental length scales (e.g., diameters) of the melt pool, that isconcentric with the melt pool. The system may further comprise a layerdispensing mechanism that includes a cyclonic separator, which layerdispensing mechanism is configured to planarize a material bed disposedadjacent to the platform, which material bed can comprise thepre-transformed material. During the printing can comprise duringformation of the melt pool. The physical attribute value may becorrelated to the temperature. The physical attribute value can comprisean amplitude, or wavelength of an electromagnetic beam that irradiatesfrom the target surface. The electromagnetic beam can comprise aninfra-red beam. The physical attribute value can comprise an amplitude,or wavelength of an electromagnetic beam that is reflected from thetarget surface. The detecting can comprise using an optical fiber thatis coupled to a detector. The first detector can be different from thesecond detector. The second detector can comprise a second detector set.The second detector set can comprise an optical fiber bundle comprisinga plurality of optical fibers. The plurality of optical fibers can beoperatively coupled to a plurality of detectors (e.g., respectively).The detecting in operation (iii) can comprise averaging the signaldetected from the second detector set to obtain the second physicalattribute value. During the printing can comprise during formation of alayer, a plurality of melt pools within a layer, or the melt pool. Thelayer can be a portion of the 3D object. The printing can comprise usinga printing instruction to control the energy beam. The system mayfurther comprise altering the printing instruction using the comparing.

The at least one characteristic of the energy beam can comprise (I) thepower density, (II) the cross-section beam, (III) the dwell time, or(IV) the focus, of the energy beam. Alter in operation (iv) can beduring the transforming to form the melt pool. Alter in operation (iv)can comprise comparing (I) the first physical attribute value with arespective first physical attribute threshold value, (II) the secondphysical attribute value with a respective second physical attributethreshold value, or (III) the first physical attribute value with thesecond physical attribute threshold value. Alter in operation (iv) canbe to control the temperature distribution profile in the volumecomprising the melt pool or the vicinity of the melt pool. The use, ordirect use of, in operation (iv) can (e.g, respectively) compriseestimate, or direct estimation of, a temperature distribution profile inthe in the volume comprising the melt pool or the vicinity of the meltpool. The use, or direct use of, in operation (iv) can (e.g,respectively) comprise adjust, or direct adjustment of, a printinginstruction of the 3D model. The use, or direct use of, in operation(iv) can (e.g, respectively) comprise alter, or direct alteration of, aphysical model of the printing. The use, or direct use of, in operation(iv) can (e.g, respectively) comprise alter, or direct alteration of, atleast one parameter of a physical model of the printing. At least two ofoperations (i) to (iv) may be directed by the same controller. At leasttwo of operations (i) to (iv) may be directed by different controllers.

An apparatus for 3D printing comprising at least one controller that isprogrammed to: (i) direct an energy beam to transform a pre-transformedmaterial to form a melt pool as part of the 3D object, wherein the atleast one controller is operatively coupled to the energy beam; (ii)direct a first detector to detect the physical-attribute of the meltpool to obtain a first physical-attribute value, wherein the at leastone controller is operatively coupled to the first detector; (iii)direct a second detector to detect the physical-attribute of a melt poolvicinity to obtain a second physical-attribute value and (iv) use, ordirect use of, the first physical-attribute value, secondphysical-attribute value, or the first physical-attribute value and thesecond physical-attribute value, to alter at least one characteristic ofthe energy beam during the printing. At least two of operations (i) to(iv) may be directed by the same controller. At least two of operations(i) to (iv) may be directed by different controllers.

A computer software product for printing a 3D object from a desiredmodel, which computer software product comprises a non-transitorycomputer-readable medium in which program instructions are stored, whichinstructions, when read by a computer, cause the computer to performoperations comprising: (a) receive an input signal from a first detectorthat measures a physical attribute of a melt pool formed by irradiatinga pre-transformed material by an energy beam, wherein the non-transitorycomputer-readable medium is operatively coupled to the first detector;(b) receive an input signal from a second detector that measures aphysical attribute of a vicinity of the melt pool, wherein thenon-transitory computer-readable medium is operatively coupled to thesecond detector; and (c) use the first physical-attribute value, secondphysical-attribute value, or the first physical-attribute value and thesecond physical-attribute value, to alter a printing instruction of the3D object. Alter a printing instruction can comprise alter at least onecharacteristic of the energy beam. Alter may be during the printing(e.g., during formation of the melt pool). Alter can comprise altering acomputer model of the printing. Alter can comprise alter at least oneparameter in the computer model.

In another aspect, a method for generating a 3D object comprises:generating in a material bed at least a first portion of a 3D object anda physical marker (e.g., flag), wherein the 3D object is generatedaccording to a model of a requested (e.g., desired) 3D structure,wherein the physical marker (e.g., flag) is an addition to the desired3D structure, wherein the three dimensional object may comprise aportion that is prone to deformation, wherein the flag is attached tothe portion that is prone to deformation; and detecting at least aportion of the physical marker (e.g., flag) (e.g., during thegenerating).

The method may further comprise altering the manner of generating atleast a second portion of the 3D object using the detecting of the atleast a portion of the physical marker. The detecting can be during thegenerating (e.g., printing). The detecting of the at least a portion ofthe physical marker (e.g., flag) can be in real time. The detection ofthe deviation can be during the generating (e.g., in real time).Detecting at least a portion of the physical marker may be during theformation of the 3D object (e.g., in real time). Detecting may be from aposition outside the material bed. Outside can comprise above. Detectingmay comprise optically detecting. Optically detecting may comprisecapturing by a camera (e.g., stills and/or video camera). Opticallydetecting may comprise lasing. Optically detecting may comprisemetrology mapping. Optically detecting may comprise a height mapping.The mapping may be a two dimensional or a 3D mapping. Opticallydetecting may comprise using an oscillating radiation beam to formrepeating projected areas of relative low and relative high intensity.Relative may be with respect to each to other. The method may furthercomprise detecting a deviation from the oscillating radiating beam. Thephysical marker (e.g., flag) may be attached to the portion that isprone to deformation at a position that is buried in the material bed(e.g., during at least a portion of the 3D object formation, such as,during the deformation of that portion). Buried may be during thedeformation of that portion (e.g., and during the printing). The methodmay further comprise controlling the deformation by the detection of theat least a portion of the physical marker. Controlling may comprisereducing. Controlling may comprise monitoring. Controlling thedeformation can comprise altering at least one characteristic of theenergy beam or of an energy source that generates the energy beam. Theat least one characteristic of the energy beam can comprise dwell time,intermission time, speed, trajectory, cross section, footprint on anexposed surface of the material bed, fluence, focus, or power density.The at least one characteristic of the energy source can comprise power.The method may further comprise detaching the physical marker (e.g.,flag) (e.g., in situ and/or in real-time). In situ may comprise in thepowder bed. In real-time may comprise during at least a portion of the3D printing, e.g., during occurrence of the deformation. The materialbed may comprise a particulate material. For example, the material bedmay be a powder bed. The powder material can be selected from at leastone member of the group consisting of metal alloy, elemental metal,ceramic, and an allotrope of elemental carbon. The material can comprisea particulate material. The particulate material can comprise at leastone member selected from the group consisting of metal alloy, elementalmetal, ceramic, an allotrope of elemental carbon, and an organicmaterial. The method may further comprise planarizing the exposedsurface of the material bed using a layer dispensing mechanismcomprising a cyclonic separator.

In another aspect, a system for printing a 3D object comprises: (e.g.,an enclosure configured to contain) a material bed; an energy sourcethat is configured to generate an energy beam, which energy beam isconfigured to transform at least a portion of the material bed into botha transformed material as part of the three dimensional object and aphysical marker, which 3D object comprises a portion that is prone todeformation, wherein the physical marker is connected to the portion,wherein the 3D object is formed according to a model of a requested 3Dstructure, wherein the physical marker is an addition to the requested3D structure, wherein upon deformation a position of the at least aportion of the physical marker deviates, wherein the energy source isoperatively coupled to the material bed; a detector that detects atleast a portion of the physical marker, wherein the detector isoperatively coupled to the material bed; and a controller operativelycoupled to the material bed, first energy source, second energy source,and detector and is programmed to: (i) direct the energy beam togenerate a first portion of the 3D object and the physical marker fromat least a portion of the material bed, (ii) evaluate any deviation fromthe position of the at least a portion of the physical marker, and (iii)use the evaluate to control at least one characteristic of the (I)energy beam, (II) energy source, or (III) energy beam and energy source,to form a second portion of 3D object. The energy source, and/ordetector may be operatively coupled to the material bed

The evaluate in operation (ii) can be during the printing. The evaluatein operation (ii) can be in real time. The physical marker can beconnected to the portion upon its formation. The at least onecharacteristic of the energy beam can comprise dwell time, intermissiontime, speed, trajectory, cross section, footprint on an exposed surfaceof the material bed, fluence, focus, or power density. The at least onecharacteristic of the energy source can comprise power. The system mayfurther comprise controlling the deformation by using the evaluate inoperation (iii). The controlling can comprise reduce. The control cancomprise monitor. The physical marker can be attached to the portionthat is prone to deformation at a position that is buried in thematerial bed, which buried is during the deformation. The material bedcan comprise a particulate material. The particulate material cancomprise at least one member selected from the group consisting of metalalloy, elemental metal, ceramic, an allotrope of elemental carbon, andan organic material. The system may further comprise a layer dispensingmechanism comprising a cyclonic separator, which layer dispensingmechanism is configured to planarize an exposed surface of the materialbed during at least a portion of the printing.

In another aspect, a system for printing a 3D object comprising: anenclosure configured to contain a material bed; an energy sourceconfigured to generate an energy beam that transforms at least a portionof the material bed into (A) a transformed material as part of the threedimensional object and (B) a physical marker, which 3D object comprisesa portion that is deformable, wherein the physical marker is connectedto the portion, wherein the 3D object is formed according to a model ofa requested 3D object, wherein the physical marker is an addition to therequested 3D object, wherein upon deformation a position of the at leasta portion of the physical marker deviates, wherein the energy source isoperatively coupled to the material bed; a detector that detects atleast a portion of the physical marker, wherein the detector isoperatively coupled to the material bed; and at least one controllerthat is operatively coupled to the material bed, first energy source,second energy source, and detector, and is separately or collectivelyprogrammed to: (i) direct the energy beam to generate a first portion ofthe 3D object and the physical marker from at least a portion of thematerial bed, and (ii) evaluate, or direct evaluation of, any deviationfrom the position of the at least a portion of the physical marker.

The at least one controller can be (separately or collectively)programmed to use the evaluate to control at least one characteristic ofthe (I) energy beam, (II) energy source, (III) energy beam and energysource, or (IV) any combination thereof, to form a second portion of 3Dobject. The evaluate or evaluation in (ii) can be during the printing.The evaluate or evaluation in (ii) can be in real time. The at least onecharacteristic of the energy beam can comprise dwell time, intermissiontime, speed, trajectory, cross section, footprint on an exposed surfaceof the material bed, fluence, focus, or power density. The at least onecharacteristic of the energy source can comprise power. The physicalmarker can be connected to the portion upon its formation (e.g, andduring the printing). The system may further comprise controlling thedeformation by using the evaluate (or evaluation) in operation (ii). Thecontroling can comprise reducing. The controlling can comprisemonitoring. The physical marker can be attached to the portion that isprone to deformation at a position that is buried in the material bed(e.g., during the printing), which buried is during the deformation. Thematerial bed can comprise a particulate material. The particulatematerial can comprise at least one member selected from the groupconsisting of metal alloy, elemental metal, ceramic, an allotrope ofelemental carbon, and an organic material. The system may furthercomprise a layer dispensing mechanism comprising a cyclonic separator,which layer dispensing mechanism is configured to planarize an exposedsurface of the material bed during at least a portion of the printing.

In another aspect, a system for forming a 3D object comprises: (e.g., anenclosure configured to contain) a material bed; an energy source thatis configured to generate an energy beam, which energy beam isconfigured to transform at least a portion of the material bed into (a)a transformed material as part of the 3D object and (b) a flag, which 3Dobject comprises a portion that is prone to deformation, wherein theflag is connected to the portion, wherein the 3D object is formedaccording to a model of a desired 3D structure, wherein the flag is anaddition to the desired 3D structure, wherein upon deformation aposition of the at least a portion of the flag deviates from an expectedposition of the at least a portion of the flag; a detector that isconfigured to detect at least a portion of the flag; and a controlleroperatively coupled to the material bed, first energy source, secondenergy source, and detector and is programmed to: (i) direct the energybeam to generate the 3D object and the flag from at least a portion ofthe material bed; (ii) evaluate any deviation from the expected positionof the at least the portion of the flag (e.g., during the forming); and(iii) using the evaluate to control at least one characteristic of theenergy beam to form the 3D object. The flag can be connected to theportion upon its formation. The expected position of the at least aportion of the flag corresponds to the attached flag to the non-deformed3D object. The flag may be a physical marker. The energy source and/orthe detector may be operatively coupled to the material bed.

In another aspect, an apparatus for forming a 3D object comprises: atleast one controller that is programmed to (a) direct disposal of amaterial bed; (b) direct an energy beam to generate a transformedmaterial from at least a portion of the material bed, which transformedmaterial forms at least a portion of the 3D object and a flag, whereinthe 3D object comprises a portion that is prone to deformation, whereinthe flag is connected to the portion that is prone to deformation; and(c) direct a detector to detect a deviation in the position of at leasta portion of the flag from an expected position of the at least aportion of the flag (e.g., during the forming), which deviation isindicative of the deformation, and wherein the at least one controlleris operatively coupled to the material bed, the detector, and the energybeam. The at least one controller may evaluate a degree of thedeformation according to the deviation. The at least one controller maydirect an alteration in at least one characteristic of the energy beamaccording to the deviation. The alteration may result in a reduceddeformation. The expected position of the at least a portion of the flagcorresponds to the attached flag to the non-deformed 3D object. The atleast one controller may comprise a plurality of controllers. At leasttwo of (a) to (c) may be directed by the same controller. At least twoof (a) to (c) may be directed by different controllers.

In another aspect, a computer software product for forming at least one3D object, comprises a non-transitory computer-readable medium in whichprogram instructions are stored, which instructions, when read by acomputer, cause the computer to perform operations comprising: (a)receive a first input signal from a sensor that comprises a location ofat least a portion of a flag that is connected to at least a portion ofthe 3D object (e.g., during the forming), which portion is prone todeformation, which 3D object is buried at least in part in the materialbed; (b) receive a second input signal (e.g., during the forming) fromthe sensor that comprises a deviation from the location of the at leasta portion of the flag; and (c) compare the first input signal with thesecond input signal to generate a result, which result is indicative ofa deformation of the portion of the 3D object. The computer softwareproduct may further cause the computer to perform operations comprising:directing an energy beam to alter at least one characteristic of theenergy beam based on the result, which energy beam transforms at least aportion of the material bed to form at least a portion of the 3D object,wherein the non-transitory computer-readable medium is operativelycoupled to the energy beam. The non-transitory computer-readable mediumcan be operatively coupled to the energy beam. Compare may be duringformation of the 3D object.

In another aspect, a method for forming (e.g., printing) at least one 3Dobject comprises: (a) generating the at least one 3D object in amaterial bed, wherein the top surface of the 3D object is buried atleast in part in the material bed, which material bed comprises anexposed surface having an average planar surface, wherein the at leastone 3D object causes at least a portion of the exposed surface todeviate from the average planar surface; (b) projecting a detectableshape (e.g., projecting an image of a detectable shape) on the exposedsurface using a scanning energy beam; and (c) detecting a deviation inthe detectable shape from an expected shape (e.g., during the forming,e.g., during the printing).

The shape may be projected on the exposed surface. The method mayfurther comprise controlling (e.g., altering) the function of one ormore components (e.g., mechanism) of the printing using the deviation.The top surface of the 3D object can be buried (e.g., at least in part)in the material bed. Detecting may comprise optically detecting. Thedeviation in the shape may comprise intensity deviation. The deviationin the (e.g., projected and subsequently detected) shape may comprisefrequency deviation. The deviation in the shape may comprise deviationin a fundamental length scale (FLS) of the shape. The deviation may bein the type of shape (e.g., the expected shape may be a rectangle andthe detected shape may be an oval). The shape may be an area that isprojected on the exposed surface of the material bed. The FLS maycomprise a cross section, shape, or area. The FLS may comprise a length,or width. The shape projected on the exposed surface of the material bedmay comprise a region having a first intensity that is detectablydifferent from an area that does not occupy the projected shape, havinga second intensity (e.g., that has (e.g., substantially) no detectableradiation of the scanning energy beam). The first intensity can behigher than the second intensity, which higher is detectable. Detectablemay comprise optically detectable. The deviation may comprise deviationin the shape type (e.g., deviation in shape from an expected rectangularshape). The deviation may comprise deviation in the first intensity orsecond intensity. The deviation can be used in detecting a position ofthe 3D object (e.g., in the material bed. For example, with respect tothe exposed surface of the material bed). The position may comprise avertical or horizontal position. The deviation can be used in detectinga deformation in the 3D object. The deviation can be used in detectingand/or assessing a deformation in the top surface of the 3D object. Thedeviation can be used in detecting and/or assessing a deformation in thetop surface of the 3D object. The shape type and/or its position withrespect to the exposed surface, may vary in time. The position of thescanning shape with respect to the exposed surface may vary as afunction of time. The shape may appear traveling on the exposed surface(e.g., over time). The projected shape type (e.g., area on the targetsurface that is occupied by the projected shape) may vary over time. Theprojected shape type may be (e.g., substantially) constant over time.The shape may vary in different areas of the exposed surface. Theprojected shape may be (e.g., substantially) the same over the (e.g.,entire) exposed surface. The projected shape may compriseelectromagnetic radiation. The projected shape may comprise a firstwavelength that is different from a second wavelength of a transformingenergy beam used in the formation of the 3D object. The shape may beprojected at a first angle onto the exposed surface, and thetransforming energy beam may be projected at a second angle onto theexposed surface. The first angle may be different from the second angle.The first angle may be (e.g., substantially) the same as the secondangle. The scanning energy beam producing the projected shape may beseparated from a transforming energy beam that is used in the formationof the 3D object. Separated may be in terms of location and/orwavelength. Separated may be in terms of detection. Separated may be interms of beam trajectory. The scanning energy beam may coincide with thetransforming energy beam. Coincide may be in terms of trajectory.

In another aspect, a system for forming a 3D object comprises: amaterial bed (e.g., disposed in an enclosure configured to contain it)comprising an exposed surface having an average planarity; a firstenergy source that generates (e.g., is configured to generate) a firstenergy beam, which first energy beam transforms (e.g., is configured totransform) at least a portion of the material bed into a transformedmaterial as part of the 3D object, which 3D object is buried at least inpart in the material bed, wherein the 3D object causes at least aportion of the exposed surface to deviate from the average planarity(wherein the first energy source is operatively coupled to the materialbed); a second energy source that is configured to generate a secondenergy beam, which second energy beam is configured to project adetectable-shape on the exposed surface (wherein the second energysource is operatively coupled to the material bed); a detector that isconfigured to detect a deviation between an expected shape of thedetectable-shape and a detected shape of the detectable-shape, whereinthe detected is from the exposed surface (wherein the detector isoperatively coupled to the material bed); and a controller (or at leastone controller) that is operatively coupled to the material bed, firstenergy source, second energy source, and detector, and is programmed to:(i) direct the first energy beam to generate the 3D object from at leasta portion of the material bed; (ii) direct the second energy beam togenerate the detectable-shape (e.g., during the forming); (iii) evaluatethe deviation to produce a result.

The controller (or at least one controller) may further be programmed to(iv) use (e.g., at least in part) the result to control at least onecharacteristic of the first energy beam and/or at least one mechanism toform the 3D object. The system may comprise controlling (e.g., altering)the function of one or more components (e.g., mechanism) of the printingusing the evaluation. Use in operation (iv) may be in real time duringthe formation of the 3D object. The first energy source may be differentfrom the second energy source. The first energy source and second energysource may be the same energy source. The first energy beam may bedifferent from the second energy beam. The first energy source may have(e.g., substantially) the same characteristics as the second energysource. The first energy beam may have (e.g., substantially) the samecharacteristics as the second energy beam. The first energy beam mayhave different characteristics as compared to the second energy beam. Atleast two of the at least one controller programed to effectuate (i) to(iv), may be the same controller. The at least one controller may be aplurality of controllers. At least two of the at least one controllerprogramed to effectuate (i) to (iv), may be different controllers. Thesecond energy beam, the first energy beam, or both the first energy beamand the second energy beam, may comprise electromagnetic radiation. Thefirst energy beam may be a laser beam. The second energy beam may be alight emitting diode beam. The second energy beam may be a visible lightbeam. The first energy beam may comprise a laser beam. The second energybeam may comprise a LED. The second energy source may comprise a digitalmirror.

In another aspect, an apparatus for detecting a 3D object comprises: amaterial bed comprising an exposed surface having an average planarity;a first energy source configured to generate a first energy beam, whichfirst energy is configured to transform at least a portion of thematerial bed into a transformed material as part of the 3D object, which3D object is buried at least in part in the material bed, wherein the 3Dobject causes at least a portion of the exposed surface to deviate fromthe average planarity, wherein the first energy source is operativelycoupled and/or disposed adjacent to the material bed; a second energysource configured to generate (e.g., during formation of thethree-dimensional object) a second energy beam, which second energy beamthat is configured to project a detectable-shape on the exposes surface,wherein the second energy source is operatively coupled and/or disposedadjacent to the material bed; and a detector that is configured todetect a deviation between an expected shape of the detectable-shape anda detected shape of the detectable-shape, which deviation is indicativeof a change from a requested structure and/or position of the 3D object.The change may be indicative of a deformation in at least a portion ofthe 3D object. The apparatus may comprise using the deviation to control(e.g., alter) the function of one or more components (e.g., mechanism)of the formation of the 3D object (e.g., as part of the transformation).

In another aspect, a computer software product for forming at least one3D object, comprises a non-transitory computer-readable medium in whichprogram instructions are stored, which instructions, when read by acomputer, cause the computer to perform operations comprising: (a)receive a first input signal from a sensor that comprises adetectable-shape that is projected on an exposed surface of a materialbed, wherein the non-transitory computer-readable medium is operativelycoupled to the sensor; (b) receive a second input signal from the sensorthat comprises a deviation between an expected shape of thedetectable-shape and a detected shape of the detectable-shape (e.g.,during the forming), wherein the material bed comprises at least aportion of a 3D object that is buried at least in part in the materialbed; and (c) compare the first input signal with the second input signalto generate a result, which result is indicative of a change from arequested structure or position of the 3D object. The computer softwareproduct may further cause the computer to perform operations comprising:direct an energy beam to alter at least one characteristic of the energybeam based on the result, which energy beam transforms at least aportion of the material bed to form at least a portion of the 3D object.The non-transitory computer-readable medium may be operatively coupledto the energy beam. The non-transitory computer-readable medium may beoperatively coupled to the energy beam. Compare may be during formationof the 3D object. The operations may comprise using the result tocontrol (e.g., alter) the function of one or more components (e.g.,mechanism) of the formation of the 3D object. The computer softwareproduct may further cause the computer to perform operations comprising:direct a mechanism of the forming to alter at least one characteristicbased on the result. The mechanism may comprise a layer dispensingmechanism, or an optical system. The projected scanning energy beam maytranslate along at least a portion of the exposed surface over time. Thedetectable-shape may translate along the exposed surface over time. Theexpected shape of the detectable-shape may remain unaltered over time.The expected shape of the detectable-shape may change (e.g., in a knownand/or predetermined way) over time.

In another aspect, a method for forming (e.g., printing) at least one 3Dobject comprises: (a) generating the at least one 3D object in amaterial bed, wherein the top surface of the 3D object is buried atleast in part in the material bed, which material bed comprises anexposed surface having an average planar surface, wherein the at leastone 3D object causes at least a portion of the exposed surface todeviate from the average planar surface; (b) projecting an oscillatingbeam on the exposed surface, which oscillating beam comprises adetectable oscillation pattern; and (c) detecting a deviation in thedetectable oscillation pattern (e.g., during the forming).

The method may further comprise controlling (e.g., altering) thefunction of one or more components (e.g., mechanism) of the printingusing the deviation. The top surface of the 3D object can be buried(e.g., at least in part) in the material bed. Detecting may compriseoptically detecting. The deviation in the oscillation pattern maycomprise intensity deviation. The deviation in the oscillation patternmay comprise frequency deviation. The deviation in the oscillationpattern may comprise deviation in a fundamental length scale (FLS) of arepeating area within the oscillating pattern. The repeating area can bean area that is projected on the exposed surface of the material bed.The FLS may comprise a cross section, shape, or area. The FLS maycomprise a length, or width. The oscillation pattern projected on theexposed surface of the material bed may comprise a region having a firstintensity and a first shape and a region having a second intensity and asecond shape. The first intensity can be higher than the secondintensity, which higher is detectable. Detectable may comprise opticallydetectable. The deviation may comprise deviation in the first shape orsecond shape. The deviation may comprise deviation in the firstintensity or second intensity. The deviation can be used in detecting aposition of the 3D object (e.g., in the material bed. E.g., with respectto the exposed surface of the material bed). The position may comprise avertical or horizontal position. The deviation can be used in detectinga deformation in the 3D object. The deviation can be used in detecting adeformation in the top surface of the 3D object. The deviation can beused in detecting a deformation in the top surface of the 3D object. Themethod may further comprise detecting a deviation in the first intensityor in the second intensity. The oscillating beam may alter in time. Theprojected oscillating pattern may vary as a function of time. Theoscillating beam may appear traveling on the exposed surface (e.g., overtime). The oscillating beam may vary over time. The oscillating beam maybe (e.g., substantially) constant over time. The oscillating beam mayvary in different areas of the exposed surface. The oscillating beam maybe (e.g., substantially) the same over the (e.g., entire) exposedsurface. The oscillating beam may comprise electromagnetic radiation.The oscillating beam may comprise a first wavelength that is differentfrom a second wavelength of a transforming energy beam used in theformation of the 3D object. The oscillating beam may be projected at afirst angle onto the exposed surface, and the transforming energy beammay be projected at a second angle onto the exposed surface. The firstangle may be different from the second angle. The first angle may be(e.g., substantially) the same as the second angle. The oscillating beammay be separated from a transforming energy beam that is used in theformation of the 3D object. Separated may be in terms of location and/orwavelength. Separated may be in terms of detection. Separated may be interms of beam trajectory. The oscillating beam may coincide with thetransforming energy beam. Coincide may be in terms of trajectory.

In another aspect, a system for forming a 3D object comprises: amaterial bed (e.g., disposed in an enclosure configured to contain it)comprising an exposed surface having an average planarity; a firstenergy source that generates (e.g., is configured to generate) a firstenergy beam, which first energy beam transforms (e.g., is configured totransform) at least a portion of the material bed into a transformedmaterial as part of the 3D object, which 3D object is buried at least inpart in the material bed, wherein the 3D object causes at least aportion of the exposed surface to deviate from the average planarity(wherein the first energy source is operatively coupled to the materialbed); a second energy source that is configured to generate a secondenergy beam, which second energy beam is an oscillating beam that isconfigured to project on the exposed surface and is configured to format least one detectable pattern (wherein the second energy source isoperatively coupled to the material bed); a detector that is configuredto detect a deviation from the detectable pattern (wherein the detectoris operatively coupled to the material bed); and a controller (or atleast one controller) that is operatively coupled to the material bed,first energy source, second energy source, and detector, and isprogrammed to: (i) direct the first energy beam to generate the 3Dobject from at least a portion of the material bed; (ii) direct thesecond energy beam to generate the detectable pattern (e.g., during theforming); (iii) evaluate the deviation from the detectable pattern; and(iv) using (e.g., at least in part) the evaluation (e.g., evaluate) tocontrol at least one characteristic of the first energy beam to form the3D object.

The system may comprise controlling (e.g., altering) the function of oneor more components (e.g., mechanism) of the printing using theevaluation. Using in operation (iv) may be in real time during theformation of the 3D object. The first energy source may be differentfrom the second energy source. The first energy source and second energysource may be the same energy source. The first energy beam may bedifferent from the second energy beam. The first energy source may have(e.g., substantially) the same characteristics as the second energysource. The first energy beam may have (e.g., substantially) the samecharacteristics as the second energy beam. The first energy beam mayhave different characteristics as compared to the second energy beam. Atleast two of the at least one controller programed to effectuate (i) to(iv), may be the same controller. The at least one controller may be aplurality of controllers. At least two of the at least one controllerprogramed to effectuate (i) to (iv), may be different controllers. Thesecond energy beam, the first energy beam, or both the first energy beamand the second energy beam, may comprise electromagnetic radiation. Thefirst energy beam may be a laser beam. The second energy beam may be alight emitting diode beam. The second energy beam may be a visible lightbeam. The first energy beam may comprise a laser beam. The second energybeam may comprise a LED. The second energy source may comprise a digitalmirror.

In another aspect, a system for printing a three-dimensional objectcomprises: an enclosure configured to contain a material bed comprisingan exposed surface having an average planarity; a first energy sourcethat is configured to generate a first energy beam that transforms atleast a portion of the material bed into a transformed material as partof the three-dimensional object, which three-dimensional object isburied at least in part in the material bed, wherein thethree-dimensional object causes at least a portion of the exposedsurface to deviate from the average planarity, wherein the first energysource is operatively coupled to the material bed; a second energysource that is configured to generate a second energy beam, which secondenergy beam is an oscillating beam that is projected on the exposessurface to form a detectable pattern, wherein the second energy sourceis operatively coupled to the material bed; a detector that isconfigured to detect a deviation from the detectable oscillatingpattern, wherein the detector is operatively coupled to the materialbed; and at least one controller operatively coupled to the materialbed, first energy source, second energy source, and detector and isprogrammed to: (i) direct the first energy beam to generate thethree-dimensional object from at least a portion of the material bed;(ii) direct the second energy beam to generate the detectable pattern,for example, during the forming; (iii) evaluate any deviation from thedetectable oscillating pattern; and (iv) control at least onecharacteristic of the first energy beam based at least in part on anydeviation from the detectable oscillating pattern, to form thethree-dimensional object. Control in operation (iv) may be in real timeduring the formation of the three-dimensional object. The second energybeam, the first energy beam, or both the first energy beam and thesecond energy beam, can comprise electromagnetic radiation. The firstenergy source can comprise a laser. The second energy source cancomprise a digital mirror. The first energy source can be different fromthe second energy source. The first energy beam can be different fromthe second energy beam. The oscillating beam can comprise a firstwavelength that is different from a second wavelength of a transformingenergy beam used in the formation of the 3D object. The oscillating beamcan be projected at a first angle onto the exposed surface, and thetransforming energy beam may be projected at a second angle onto theexposed surface. The first angle may be different from the second angle.The second energy beam can be separated from the first energy. Separatedcan be in terms of location, wavelength, detection, beam trajectory, orany combination thereof. At least two of (i) to (iv) may be performed bythe same controller. At least two of (i) to (iv) may be performed bydifferent controllers.

In another aspect, an apparatus for detecting a 3D object comprises: amaterial bed comprising an exposed surface having an average planarity;a first energy source configured to generate a first energy beam, whichfirst energy is configured to transform at least a portion of thematerial bed into a transformed material as part of the 3D object, which3D object is buried at least in part in the material bed, wherein the 3Dobject causes at least a portion of the exposed surface to deviate fromthe average planarity, wherein the first energy source is operativelycoupled and/or disposed adjacent to the material bed; a second energysource configured to generate (e.g., during formation of thethree-dimensional object) a second energy beam, which second energy beamis an oscillating beam that is configured to project on the exposessurface to form at least a detectable pattern, wherein the second energysource is operatively coupled and/or disposed adjacent to the materialbed; and a detector that is configured to detect a deviation from thedetectable pattern, which deviation is indicative of a change from adesired structure and/or position of the 3D object. The change may beindicative of a deformation in at least a portion of the 3D object. Theapparatus may comprise using the deviation to control (e.g., alter) thefunction of one or more components (e.g., mechanism) of the formation ofthe 3D object (e.g., as part of the transformation).

In another aspect, an apparatus for forming a 3D object comprises: acontroller (e.g., or at least one controller) that is programmed todirect: (a) disposal of a material bed having an average planar exposedsurface; (b) a first energy beam to generate a transformed material fromat least a portion of the material bed as part of the three dimensionalobject, which 3D object is buried at least in part in the material bed,wherein the 3D object causes at least a portion of the exposed surfaceto deviate from the average planarity; (c) a second energy beam togenerate a pattern projected on the exposed surface (e.g., during theforming); and (e) a detector to detect a deviation from the pattern onthe exposed surface, which deviation is indicative of a change from adesired structure or position of the 3D object, and wherein thecontroller is operatively coupled to the material bed, the detector, thefirst energy beam, and the second energy beam. At least two of the atleast one controller directing (a) to (e), may be the same controller.At least two of the at least one controller directing (a) to (e), may bedifferent controllers. The at least one controller may be a plurality ofcontrollers. The apparatus may comprise using the deviation to control(e.g., alter) the function of one or more components (e.g., mechanism)of the formation of the 3D object.

In another aspect, a computer software product for forming at least one3D object, comprises a non-transitory computer-readable medium in whichprogram instructions are stored, which instructions, when read by acomputer, cause the computer to perform operations comprising: (a)receive a first input signal from a sensor that comprises a patternprojected on an exposed surface of a material bed, wherein thenon-transitory computer-readable medium is operatively coupled to thesensor; (b) receive a second input signal from the sensor that comprisesa deviation from the pattern projected on the exposed surface of thematerial bed (e.g., during the forming), wherein the material bedcomprises at least a portion of a 3D object that is buried at least inpart in the material bed; and (c) compare the first input signal withthe second input signal to generate a result, which result is indicativeof a change from a desired structure or position of the 3D object. Thecomputer software product may further cause the computer to performoperations comprising: direct an energy beam to alter at least onecharacteristic of the energy beam based on the result. The energy beammay transform at least a portion of the material bed to form at least aportion of the 3D object. The non-transitory computer-readable mediummay be operatively coupled to the energy beam. The non-transitorycomputer-readable medium may be operatively coupled to the energy beam.Compare may be during formation of the 3D object. The operations maycomprise using the result to control (e.g., alter) the function of oneor more components (e.g., mechanism) of the formation of the 3D object.The computer software product may further cause the computer to performoperations comprising: direct an energy beam to alter the function of atleast one mechanism of the forming based on the result.

In another aspect, a method for generating a 3D object comprises: (a)generating a first portion of a first layer as part of the 3D object by3D printing; (b) performing a measurement of at least one position of anexposed surface during the 3D printing; (c) assessing an alteration ofat least one characteristic of the 3D printing based on the measuring,which assessing is during the 3D printing; and (d) generating a secondportion of the first layer or of a second layer as part of the 3D objectby the 3D printing, which generating is according to a result of theassessing.

The second layer can be different from the first layer. The second layercan be subsequent to the first layer. Subsequent can be directlysubsequent. The at least a portion of the first layer can be in contactwith at least a portion of the second layer. The at least a portion ofthe first portion can be in contact with at least a portion of thesecond portion. The 3D printing can be a powder based 3D printing. Thepowder can comprise elemental metal, metal alloy, ceramics, or anallotrope of elemental carbon. The 3D printing can comprise fusing thepowder. The fusing can comprise melting or sintering. The fusing cancomprise using an energy beam to fuse at least a portion of the powderto form a transformed material, which transformed material hardens intoa hardened material as part of the 3D object. The energy beam can be anelectromagnetic beam or a charged particle beam. The electromagneticbeam can be a laser. The charged particle beam can be an electron gun.The 3D printing can be additive manufacturing. The additivemanufacturing can comprise selective laser melting, selective lasersintering, or direct metal laser sintering. The first portion can bedisposed in a material bed and wherein the exposed surface can comprisean exposed surface of the material bed. The first portion can bedisposed in a material bed and wherein the exposed surface can comprisean exposed surface of the 3D object. The exposed surface of the 3Dobject can comprise an exposed surface of the first portion. Theperforming a measurement can comprise in-situ performing themeasurement. The performing a measurement can comprise performing themeasurement in real time during the 3D printing. The performing ameasurement can comprise optically measuring. The optical measuring cancomprise using a photosensitive material that alters at least one of itsproperties as a response to radiation. The photosensitive material cancomprise p-doped metal-oxide-semiconductor (MOS), or complementary MOS(CMOS). The optical measuring can comprise using a charge-coupled device(CCD) camera. The optical measuring can comprise using superimposedwaves. The optical measuring can comprise using an interferometer. Theperforming a measurement can comprise measuring a temperature of the atleast one position. The performing a measurement can comprise measuringa location and a temperature of the at least one position. Theperforming a measurement can comprise performing a location measurementof at the at least one position. The positon can comprise vertical orhorizontal position. Performing a measurement can comprise measuring acurvature of the at least one position. Performing a measurement can beat a frequency of at least about every one second (1 Hertz). Performinga measurement can comprise scanning the exposed surface with a scanningenergy beam. The scanning energy beam may comprise a shape. The scanningenergy beam may comprise a fluctuating pattern. The fluctuating patternmay fluctuate in time and/or space. The scanning energy beam may producea fluctuating pattern on the exposed surface. The scanning energy beammay comprise a detectable radiation. The assessing may comprisecomparing a detected shape of the scanning energy beam, with an expectedshape of the scanning energy beam to produce a result. The method mayfurther comprise control at least one characteristic of the 3D printingbased on the result. The at least one characteristic may comprisecontrolling the layer dispensing mechanism (e.g., material dispenser,leveling mechanism, and/or material removal mechanism), energy beam,energy source, and/or optical system. The assessing can comprise using aprocessing unit to process at least one signal obtained from themeasuring to generate the result. The processing unit generates theresult during a time of at most one minute. The process can compriseimage processing. The assessing can comprise generating a map based onthe measuring of the at least one position. The map can be a topologicalmap. The map can be a temperature map. The map can be a map of thematerial bed, exposed surface of the material bed, 3D object, layer ofhardened material, melt pool, or any combination thereof The topologicalmap may be formed using a metrological sensor. The metrological sensormay comprise projection of a striped pattern. The metrological sensormay comprise a fringe projection profilometry device. The metrologicalsensor may be a height mapper. The metrological sensor may comprise asensing energy beam (e.g., emitter) and a receiver. The emitter maycomprise a projector. The emitter may project the sensing energy beam ona target surface. The target surface may comprise an expose surface of amaterial bed, a layer of hardened material, a 3D object, or a melt pool.The sensing energy beam may form a pattern on the exposed surface. Thepattern may comprise areas of various levels of light intensity. Thelight intensity profile may comprise an on off pattern. The lightintensity profile may comprise a fluctuating pattern. The fluctuatingpattern may comprise gradually fluctuating intensity pattern or abruptlyfluctuating intensity pattern. The fluctuating pattern may be asuperposition of a multiplicity of sinusoidal waves. The fluctuatingpattern may be a superposition of a multiplicity of frequency functions(e.g., sine function and/or cosine function). The fluctuating patternmay comprise a superposition of a sinusoidal wave a decreasing function.The decreasing function may be decreasing linearly, logarithmically,exponentially, or any combination thereof The fluctuating pattern maycomprise multiplicity of functions (e.g., that are superpositioned). Themultiplicity of functions may be shifted (e.g., by a phase). Thedetector may comprise a multiplicity of sensing energy beam. Themultiplicity of energy beams may form an interference pattern. Thefluctuating pattern may comprise an interference pattern. The projectedsensing energy beams may be of the same or of different colors. Theprojected sensing energy beams may be of the same or of differentfrequencies. The various multiplicity of projected sensing energy beamsmay be projected simultaneously or sequentially. A detection system maycomprise a multiplicity of detectors (e.g., a multiplicity of receiversand/or transmitters). The multiplicity of receivers and/or transmittersmay view the target location from a multiplicity of spatial position.The multiplicity of spatial positions may form a multi perspectiveimage. The metrological detector (e.g., height mapper) may determine auniformity of the target surface (e.g., exposed surface of the powderbed, 3D object, or melt pool). The uniformity may comprise standarddeviation, mean, or average height of target surface. The uniformity maycomprise height skew, trend, or step within the target surface. Themetrological detector may differentiate between uniformity along thelength and the width of the powder bed. The length of the powder bed maybe a direction along which the layer dispenser mechanism translates. Thewidth of the powder bed may be a direction perpendicular to thedirection along which the layer dispenser mechanism translates.

The 3D printing can comprise using an energy beam to transform at leasta portion of a material bed to form a transformed material as part ofthe 3D object. The transformation operation may be melt, sinter, orsolidify. The at least one characteristic can comprise an areatransformed by the energy beam. The at least one characteristic cancomprise the size of a melt pool in the transformed material. The atleast one characteristic can be of the energy beam, or material bed. Theat least one characteristic can comprise the relative position of theenergy beam and the material bed. The at least one characteristic cancomprise the temperature of the material bed. The at least onecharacteristic of the energy beam can comprise its translational speed,translational acceleration, beam focus, hatching, path, wavelength,energy per unit area, power, cross section, cross sectional energyprofile, or homogeneity. The homogeneity characteristics can comprisehomogeneity of the energy flux over dwell time, or across a crosssection of the energy beam. The 3D printing further can comprisealtering the relative position between the energy beam and the materialbed using a scanner, and wherein the at least one characteristic cancomprise a characteristics of the scanner. The at least onecharacteristic of the scanner can comprise its translational speed,acceleration, path, or hatching. The path characteristics can comprisepath continuity, curvature, or direction. The hatch characteristics cancomprise hatch spacing, curvature, or direction. The at least oneposition comprise substantially all positions of the exposed surface.The at least one position can be at a distance of about one millimeteraway from the energy beam. The performing a measurement may furthercomprise measuring a temperature of the transformed material at oradjacent to its interaction with the energy beam. The at least onecharacteristic can comprise the energy per unit area of the energy beam.The 3D printing can comprise using an energy beam to transform at leasta portion of a material bed to form a transformed material as part ofthe second portion, and wherein the at least one characteristic cancomprise the fundamental length scale of the transformed material. The3D printing can comprise using an energy beam to transform at least aportion of a material bed to form a transformed material as part of thesecond portion, and wherein the at least one characteristic comprisesthe fundamental length scale of a melt pool formed in the transformedmaterial. The alteration of the at least one characteristic of the 3Dprinting may comprise altering at least one characteristic of ageneration device that is used to generate the at least one 3D object.The generation device may generate the 3D object under at least oneformation parameter in the 3D printing. Altering at least onecharacteristic may comprise altering at least one formation parameter ofthe generation device. The formation parameter may be a parameterrelated to the forming of the 3D object.

In another aspect, a system for printing at least one 3D object,comprises: (a) a platform that accepts a material bed, wherein duringuse, at least a portion of the material bed is used to generate at leastone 3D object, wherein the material bed is adjacent to the platform; (b)a device that generates a signal, which device comprises a first sensorthat senses one or more input signals and generates a first outputsignal, which signal is generated during the generation of a firstportion of (e.g., a first layer as part of) the 3D object; (c) ageneration device used to generate the 3D object under at least oneformation parameter using 3D printing, wherein the generation device isdisposed adjacent to the material bed; and (d) a controller comprising aprocessing unit that is programed to: (i) process the output signal togenerate a result indicative of the formation parameter during thegeneration of the first layer as part of the 3D object; and (ii) directthe generation device to alter a function of the generation device basedon the result during the generation of a second portion of the firstlayer or of a second layer as part of the 3D object. The generationdevice can comprise an energy beam or a material bed. The generationdevice can comprise a scanner. The generation device can comprise alayer dispensing mechanism or a heat sink.

In another aspect, an apparatus for printing one or more 3D objectscomprises a controller that is programmed to: (a) direct a processingunit to process an output signal received from a sensor and generate aresult indicative of a formation parameter during formation of a firstportion (e.g., layer) as part of the 3D object formed by a 3D printingmethodology, wherein the sensor senses an input signal during formationof a first portion of the first layer, wherein the controller isoperatively coupled to the sensor, and to the processing unit; and (b)direct a mechanism used in the 3D printing (e.g., methodology) to altera function of the mechanism based on the result before or duringformation of a second portion (e.g., of the first layer or of a secondlayer) of the three-dimensional object, wherein the controller isoperatively coupled to the mechanism.

In another aspect, a device comprises: a computer-readable medium andone or more processors that are coupled to the computer-readable mediumand that are configured to cause the device to: (a) obtain a first tapevent that was generated in response to receiving a message from atleast one sensing device through a first communication channel, whichsensing device senses a first exposed surface, which one or moreprocessors are operatively coupled to the at least one sensing devicethrough the first communication channel; (b) extract a firstsensing-device identifier from the first tap event; (c) obtain a secondtap event that was generated in response to receiving a message from theat least one sensing device through the first communication channel,which second tap event is obtained from a second exposed surface, whichsecond tap event is obtained during formation of a first portion of afirst layer as part of the 3D object that is generated by 3D printing;(d) extract a second sensing-device identifier from the second tapevent; (e) compare the second sensing-device identifier to the firstsensing-device identifier to determine a variations; and (f) sendthrough a second communication channel a printing-alteration-operationrequest to at least one mechanism used in the 3D printing to alter atleast one function of the mechanism based on the variation, whichprinting-alteration-operation request is sent before or during formationof a second portion of the first layer or of a second layer as part ofthe three dimensional object, wherein the one or more processors areoperatively coupled to the mechanism through the second communicationchannel The sensing device comprises a positional or a temperaturesensor. The mechanism can comprise an energy beam. The message can be asensor output. The “compare” operation may comprise image comparison.

In another aspect, a computer program product comprises a non-transitorycomputer-readable medium having computer code thereon for manipulating a3D printing process, the computer code comprising: (a) a first programcode for receiving at least one first input from a sensor, wherein thesensor generates the first input signal before formation of a firstportion of the first layer as at least a portion of a three dimensionalobject formed by the three dimensional printing process, wherein thenon-transitory computer-readable medium is operatively coupled to thesensor; (b) a second program code for receiving at least one secondinput from a sensor, wherein the sensor generates the second inputsignal during formation of the first portion (e.g., of the first layer);(c) a third program code for comparing the first input signal with thesecond input signal and generate a result; and (d) a fourth program codefor directing a mechanism used in the 3D printing process to alter afunction of the mechanism based on the result before or during formationof a second portion (e.g., of the first layer or of a second layer) ofthe three dimensional object formed by the three dimensional printingprocess, wherein the non-transitory computer-readable medium isoperatively coupled to the mechanism.

In another aspect, a computer software product, comprising anon-transitory computer-readable medium in which program instructionsare stored, which instructions, when read by a computer, cause thecomputer to perform operations comprising: (a) receive a first inputsignal from a sensor, wherein the sensor generates the first inputsignal before formation of a first portion of the (e.g., first layer asat least a portion of the) three dimensional object formed by a threedimensional printing process, wherein the non-transitorycomputer-readable medium is operatively coupled to the sensor; (b)receive a second input signal from a sensor, wherein the sensorgenerates the second input signal during formation of the first portion(e.g., of the first layer); (c) compare the first input signal with thesecond input signal and generate a result; and (d) direct a mechanismused in the 3D printing process to alter a function of the mechanismbased on the result before or during formation of a second portion ofthe (e.g., first layer or of a second layer of the) three dimensionalobject formed by the three dimensional printing process, wherein thenon-transitory computer-readable medium is operatively coupled to themechanism.

In another aspect, a method for generating a 3D object comprises: (a)generating a first portion (e.g., of a first layer as part) of the 3Dobject by 3D printing; (b) performing a measurement of at least oneposition of the exposed surface during the 3D printing; (c) assessing analteration of at least one characteristic of the 3D printing based onthe measuring, which assessing is during the 3D printing; and (d)generating a second portion (e.g., of the first layer or of a secondlayer as part) of the 3D object by the 3D printing, which generating isaccording to a result of the assessing.

The second layer can be different from the first layer. The second layercan be subsequent to the first layer. Subsequent can be directlysubsequent. The at least a portion of the first layer can be in contactwith at least a portion of the second layer. The at least a portion ofthe first portion can be in contact with at least a portion of thesecond portion. The 3D printing can be a powder based 3D printing. Thepowder can comprise elemental metal, metal alloy, ceramics, or anallotrope of elemental carbon. The 3D printing can comprise fusing thepowder. The fusing can comprise melting or sintering. The fusing cancomprise using an energy beam to fuse at least a portion of the powderto form a transformed material, which transformed material hardens intoa hardened material as part of the 3D object. The energy beam can be anelectromagnetic beam or a charged particle beam. The electromagneticbeam can be a laser. The charged particle beam can be an electron gun.The 3D printing can be additive manufacturing. The additivemanufacturing can comprise selective laser melting, selective lasersintering, or direct metal laser sintering. The first portion can bedisposed in a material bed and wherein the exposed surface can comprisean exposed surface of the material bed. The first portion can bedisposed in a material bed and wherein the exposed surface can comprisean exposed surface of the 3D object. The exposed surface of the 3Dobject can comprise an exposed surface of the first portion. Theperforming a measurement can comprise in-situ performing themeasurement. The performing a measurement can comprise performing themeasurement in real time during the 3D printing. The performing ameasurement can comprise optically measuring. The optical measuring cancomprise using a photosensitive material that alters at least one of itsproperties as a response to radiation. The photosensitive material cancomprise p-doped metal-oxide-semiconductor (MOS), or complementary MOS(CMOS). The optical measuring can comprise using a charge-coupled device(CCD) camera. The optical measuring can comprise using superimposedwaves. The optical measuring can comprise using an interferometer. Theperforming a measurement can comprise measuring a temperature of the atleast one position. The performing a measurement can comprise measuringa location and a temperature of the at least one position. Theperforming a measurement can comprise performing a location measurementof at the at least one position. The positon can comprise vertical orhorizontal position. The performing a measurement can comprise measuringa curvature of the at least one position. The performing a measurementcan be at a frequency of at least about every one second (1 Hertz). Theassessing can comprise using a processing unit to process at least onesignal obtained from the measuring to generate the result. Theprocessing unit generates the result during a time of at most oneminute. The process can comprise image processing. The assessing cancomprise generating a map based on the measuring of the at least oneposition. The map can be a topological map. The map can be a temperaturemap. The map can be a map of the material bed, exposed surface of thematerial bed, 3D object, layer of hardened material, melt pool, or anycombination thereof

The topological map may be formed using a metrological sensor. Themetrological sensor may comprise projection of a striped pattern. Themetrological sensor may comprise a fringe projection profilometrydevice. The metrological sensor may be a height mapper. The metrologicalsensor may comprise a sensing energy beam (e.g., emitter) and areceiver. The emitter may comprise a projector. The emitter may projectthe sensing energy beam on a target surface. The target surface maycomprise an expose surface of a material bed, a layer of hardenedmaterial, a 3D object, or a melt pool. The sensing energy beam may forma pattern on the exposed surface. The pattern may comprise areas ofvarious levels of light intensity. The light intensity profile maycomprise an on off pattern. The light intensity profile may comprise afluctuating pattern. The fluctuating pattern may comprise graduallyfluctuating intensity pattern or abruptly fluctuating intensity pattern.The fluctuating pattern may be a superposition of a multiplicity ofsinusoidal waves. The fluctuating pattern may be a superposition of amultiplicity of frequency functions (e.g., sine function and/or cosinefunction). The fluctuating pattern may comprise a superposition of asinusoidal wave a decreasing function. The decreasing function may bedecreasing linearly, logarithmically, exponentially, or any combinationthereof The fluctuating pattern may comprise multiplicity of functions(e.g., that are superpositioned). The multiplicity of functions may beshifted (e.g., by a phase). The detector may comprise a multiplicity ofsensing energy beam. The multiplicity of energy beams may form aninterference pattern. The fluctuating pattern may comprise aninterference pattern. The projected sensing energy beams may be of thesame or of different colors. The projected sensing energy beams may beof the same or of different frequencies. The various multiplicity ofprojected sensing energy beams may be projected simultaneously orsequentially. A detection system may comprise a multiplicity ofdetectors (e.g., a multiplicity of receivers and/or transmitters). Themultiplicity of receivers and/or transmitters may view the targetlocation from a multiplicity of spatial position. The multiplicity ofspatial positions may form a multi perspective image. The metrologicaldetector (e.g., height mapper) may determine a uniformity of the targetsurface (e.g., exposed surface of the powder bed, 3D object, or meltpool). The uniformity may comprise standard deviation, mean, or averageheight of target surface. The uniformity may comprise height skew,trend, or step within the target surface. The metrological detector maydifferentiate between uniformity along the length and the width of thepowder bed. The length of the powder bed may be a direction along whichthe layer dispenser mechanism translates. The width of the powder bedmay be a direction perpendicular to the direction along which the layerdispenser mechanism translates.

The 3D printing can comprise using an energy beam to transform at leasta portion of a material bed to form a transformed material as part ofthe 3D object. The transformation operation may be melt, sinter, orsolidify. The at least one characteristic can comprise an areatransformed by the energy beam. The at least one characteristic cancomprise the size of a melt pool in the transformed material. The atleast one characteristic can be of the energy beam, or material bed. Theat least one characteristic can comprise the relative position of theenergy beam and the material bed. The at least one characteristic cancomprise the temperature of the material bed. The at least onecharacteristic of the energy beam can comprise its translational speed,translational acceleration, beam focus, hatching, path, wavelength,energy per unit area, power, cross section, cross sectional energyprofile, or homogeneity. The homogeneity characteristics can comprisehomogeneity of the energy flux over dwell time, or across a crosssection of the energy beam. The 3D printing further can comprisealtering the relative position between the energy beam and the materialbed using a scanner, and wherein the at least one characteristic cancomprise a characteristic of the scanner. The at least onecharacteristic of the scanner can comprise its translational speed,acceleration, path, or hatching. The path characteristics can comprisepath continuity, curvature, or direction. The hatch characteristics cancomprise hatch spacing, curvature, or direction. The at least oneposition comprise substantially all positions of the exposed surface.The at least one position can be at a distance of about one millimeteraway from the energy beam. The performing a measurement may furthercomprise measuring a temperature of the transformed material at oradjacent to its interaction with the energy beam. The at least onecharacteristic can comprise the energy per unit area of the energy beam.The 3D printing can comprise using an energy beam to transform at leasta portion of a material bed to form a transformed material as part ofthe second portion, and wherein the at least one characteristic cancomprise the fundamental length scale of the transformed material. The3D printing can comprise using an energy beam to transform at least aportion of a material bed to form a transformed material as part of thesecond portion, and wherein the at least one characteristic comprisesthe fundamental length scale of a melt pool formed in the transformedmaterial. The alteration of the at least one characteristic of the 3Dprinting may comprise altering at least one characteristic of ageneration device that is used to generate the at least one 3D object.The generation device may generate the 3D object under at least oneformation parameter in the 3D printing. Altering at least onecharacteristic may comprise altering at least one formation parameter ofthe generation device. The formation parameter may be a parameterrelated to the forming of the 3D object.

In another aspect, a system for printing at least one 3D object,comprises: (a) a platform that accepts a material bed, wherein duringuse, at least a portion of the material bed is used to generate at leastone 3D object, wherein the material bed is adjacent to the platform; (b)a device that generates a signal, which device comprises a first sensorthat senses one or more input signals and generates a first outputsignal, which signal is generated during the generation of a firstportion of (e.g., a first layer as part of) the 3D object; (c) ageneration device used to generate the 3D object under at least oneformation parameter using 3D printing, wherein the generation device isdisposed adjacent to the material bed; and (d) a controller comprising aprocessing unit that is programed to: (i) process the output signal togenerate a result indicative of the formation parameter during thegeneration of a first portion (e.g., layer) as part of the 3D object;and (ii) direct the generation device to alter a function of thegeneration device based on the result during the generation of a secondportion (e.g., of the first layer or of a second layer as part) of the3D object. The generation device can comprise an energy beam or amaterial bed. The generation device can comprise a scanner. Thegeneration device can comprise a layer dispensing mechanism or a heatsink. The controller can be operatively coupled to the first device, andto the second device

In another aspect, an apparatus for printing one or more 3D objectscomprises a controller that is programmed to: (a) direct a processingunit to process an output signal received from a sensor and generate aresult indicative of a formation parameter during formation of a firstlayer as part of the 3D object formed by a 3D printing methodology,wherein the sensor senses an input signal during formation of a firstportion of the first layer, wherein the controller is operativelycoupled to the sensor, and to the processing unit; and (b) direct amechanism used in the 3D printing (e.g., methodology) to alter afunction of the mechanism based on the result before or during formationof a second portion of the (e.g., first layer or of a second layer ofthe) 3D object, wherein the controller is operatively coupled to themechanism.

In another aspect, a device comprises: a computer-readable medium andone or more processors that are coupled to the computer-readable mediumand that are configured to cause the device to: (a) obtain a first tapevent that was generated in response to receiving a message from atleast one sensing device through a first communication channel, whichsensing device senses a first exposed surface, which one or moreprocessors are operatively coupled to the at least one sensing devicethrough the first communication channel; (b) extract a firstsensing-device identifier from the first tap event; (c) obtain a secondtap event that was generated in response to receiving a message from theat least one sensing device through the first communication channel,which second tap event is obtained from a second exposed surface, whichsecond tap event is obtained during formation of a first portion of afirst layer as part of the 3D object that is generated by 3D printing;(d) extract a second sensing-device identifier from the second tapevent; (e) compare the second sensing-device identifier to the firstsensing-device identifier to determine a variations; and (f) sendthrough a second communication channel a printing-alteration-operationrequest to at least one mechanism used in the 3D printing to alter atleast one function of the mechanism based on the variation, whichprinting-alteration-operation request is sent before or during formationof a second portion of the first layer or of a second layer as part ofthe 3D object, wherein the one or more processors are operativelycoupled to the mechanism through the second communication channel Thesensing device comprises a positional or a temperature sensor. Themechanism can comprise an energy beam. The message can be a sensoroutput. The “compare” operation may comprise image comparison.

In another aspect, a computer program product comprises a non-transitorycomputer-readable medium having computer code thereon for manipulating a3D printing process, the computer code comprising: (a) a first programcode for receiving at least one first input from a sensor, wherein thesensor generates the first input signal before formation of a firstportion of the first layer as at least a portion of a 3D object formedby the 3D printing process, wherein the non-transitory computer-readablemedium is operatively coupled to the sensor; (b) a second program codefor receiving at least one second input from a sensor, wherein thesensor generates the second input signal during formation of the firstportion (e.g., of the first layer); (c) a third program code forcomparing the first input signal with the second input signal andgenerate a result; and (d) a fourth program code for directing amechanism used in the 3D printing process to alter a function of themechanism based on the result before or during formation of a secondportion (e.g., of the first layer or of a second layer) of the 3D objectformed by the 3D printing process, wherein the non-transitorycomputer-readable medium is operatively coupled to the mechanism.

In another aspect, a computer software product, comprising anon-transitory computer-readable medium in which program instructionsare stored, which instructions, when read by a computer, cause thecomputer to perform operations comprising: (a) receive a (e.g., at leastone) first input signal from a sensor, wherein the sensor generates thefirst input signal before formation of a first portion of the (e.g.,first layer as at least a portion of the) 3D object formed by a 3Dprinting process, wherein the non-transitory computer-readable medium isoperatively coupled to the sensor; (b) receive a (e.g., at least one)second input signal from a sensor, wherein the sensor generates thesecond input signal during formation of the first portion (e.g., of thefirst layer); (c) compare the first input signal with the second inputsignal and generate a result; and (d) direct a mechanism used in the 3Dprinting process to alter a function of the mechanism based on theresult before or during formation of a second portion of the (e.g.,first layer or of a second layer of the) 3D object formed by the 3Dprinting process, wherein the non-transitory computer-readable medium isoperatively coupled to the mechanism (e.g., and to the sensor).

In another aspect, a method for generating at least one 3D objectcomprises: disposing a pre-transformed material (e.g., in an enclosureto form a material bed); transforming the pre-transformed material(e.g., that is at least a portion of the material bed) with an energybeam to form a transformed material portion as part of the 3D object;and controlling at least one characteristic of the energy beam in realtime during the transforming using closed loop control, wherein realtime comprises a loop sample time of at most 20 microseconds.

The pre-transformed material can be a particulate material (e.g., powdermaterial). The material bed can be a powder bed. The pre-transformedmaterial can be selected from at least one member of the groupconsisting of a metal alloy, elemental metal, ceramic, allotrope ofelemental carbon, resin, and a polymer. The pre-transformed material canbe selected from at least one member of the group consisting of a metalalloy, elemental metal, ceramic, and an allotrope of elemental carbon.The at least one characteristic of the energy beam may comprise dwelltime, cross-section, footprint, power per unit area, translation speed,fluence, flux, or intensity. The closed loop control may use a setpointcomprising a temperature, or FLS setpoint. The transformed material maycomprise a melt pool. The temperature may comprise a temperature of thematerial bed, transformed material, melt pool, a position away from afootprint of the energy beam on an exposed surface of the material bed,or any combination thereof Away may be at most about 20 millimeters awayfrom the center of the footprint. Away may be at most about 10millimeters away from the center of the footprint. Away may be at mostabout 5 millimeters away from the center of the footprint. Away may beat most about 1 millimeter away from the center of the footprint. Thetransformed material may comprise a melt pool, and wherein the FLS maycomprise a FLS of the material bed, transformed material, or melt pool.The FLS may comprise height, depth, diameter, diameter equivalence,width, or length.

In another aspect, a system for forming a 3D object comprises: apre-transformed material (e.g., that is at least a portion of a materialbed) disposed above a platform; an energy source configured to generatean energy beam that transforms the pre-transformed material (e.g., thatis at least a portion of the material bed into) a transformed materialas part of the 3D object; a sensor that is configured to (a) sense aphysical-attribute and (b) generate an output signal; and a controlleroperatively coupled to the target surface (e.g., and to the materialbed), sensor, and energy beam, and is programmed to: (i) direct theenergy beam to generate the 3D object from the transformed material(e.g., that is at least a portion of the material bed); and (ii) use theoutput signal to control at least one characteristic of the energy beamin real time during (i) by using closed loop control, wherein real timecomprises a loop sample time of at most 20 microseconds.

In another aspect, an apparatus for forming a 3D object comprises: atleast one controller that is programmed to (a) direct deposition of apre-transformed material (e.g., and thus direct generation of a materialbed); (b) direct an energy beam to generate a transformed material fromthe pre-transformed material (e.g., that is at least a portion of thematerial bed); (c) control in real time during (b) at least onecharacteristic of the energy beam by using a signal from a detector thatdetects a physical-attribute, which control comprises a closed loopcontrol that uses the signal, which closed loop control has a sampletime of at most 20 microseconds, and wherein the at least one controlleris operatively coupled to the target surface (e.g., and to the materialbed), the detector, and energy beam. At least two of (a) to (c) may beeffectuated by the same controller. At least two of (a) to (c) may beeffectuated by different controllers. The at least one controller maycomprise a plurality of controllers.

In another aspect, a computer software product for forming at least one3D object, comprises a non-transitory computer-readable medium in whichprogram instructions are stored, which instructions, when read by acomputer, cause the computer to perform operations comprising: (a)receive a first input signal from a sensor, wherein the sensor generatesthe first input signal during formation of the 3D object (e.g., in amaterial bed), wherein the sensor senses a physical-attribute relating(e.g., corresponding) to the formation of the 3D object (e.g.,corresponding to the formation of one or more melt pools), wherein theformation comprises using an energy beam to transform a pre-transformedmaterial (e.g., that is at least a portion of the material bed), whereinthe non-transitory computer-readable medium is operatively coupled tothe sensor; (b) compare the input signal with a setpoint of thephysical-attribute and generate a result; (d) direct an energy sourcethat generates the energy beam to alter at least one characteristic ofthe energy beam based on the result, which compare is (e.g., inreal-time) during the formation of the 3D object, wherein thenon-transitory computer-readable medium is operatively coupled to theenergy source; and (e) receive a second input signal from the sensor,wherein the time lapsed from receiving the first input signal toreceiving the second input signal is at most 20 microseconds. Thenon-transitory computer-readable medium may be operatively coupled tothe energy beam.

In another aspect, a system for irradiation control comprises: a targetsurface that comprises a material type; an energy source that isconfigured to generate an energy beam that is configured to transform atleast a portion of the target surface into a transformed material, whichenergy beam causes the at least a portion of the material type to partfrom the target surface; a detector that is configured to detect atemperature of the target surface; and at least one controlleroperatively coupled to the target surface, energy source, and detectorand is programmed to: (i) direct the energy beam to irradiate the targetsurface at a position; (ii) direct the detector to detect a temperatureat the position or adjacent to the position; (iii) evaluate a deviationbetween the temperature at the position and a target temperature value;and (iv) control at least one characteristic of the energy beam to alteran amount of the material type that parted from the material bed usingthe evaluate. The position may be within a footprint of the energy beamon the target surface. Adjacent to the position may comprise an areahaving a radius equal to at most about six footprint FLS (e.g.,diameters) measured from the center of the footprint. At least two of(i) to (iv) can be controlled by the same controller. At least two of(i) to (iv) can be controlled by different controllers. The energysource and/or detector may be operatively coupled to the target surface.

In another aspect, A system for 3D printing of at least one 3D objectcomprising: an energy source that is configured to generate an energybeam directed to a target surface, which energy beam transforms apre-transformed material into a transformed material as part of the 3Dobject, which energy beam optionally causes a fraction of thetransformed material to separate from the target surface; a detectorthat is configured to detect a temperature at a position of the targetsurface, wherein the detector is operatively coupled to the targetsurface; and at least one controller that is operatively coupled to thetarget surface, energy source, and detector, wherein the at least onecontroller is programmed to: (i) direct the energy beam to irradiate thepre-transformed material; (ii) use the detector to detect a temperatureat the position; (iii) evaluate a deviation between the detectedtemperature and a target temperature profile; and (iv) based at least inpart on any deviation, control at least one characteristic of the energybeam to alter an amount of the fraction that separates from the targetsurface.

The detector may be operatively coupled to the energy source. Thetemperature profile may be a single value, a temperature range, ortemperature function. The at least one controller can be programmed tocontrol the at least one characteristic of the energy beam tosubstantially eliminate or prevent separation of the fraction from thetarget surface. Substantially can be relative to the intended operationof the energy beam. Substantially can be relative to the affects thetransforms at least a portion of the pre-transformed material into atransformed material. At least two of (i) to (iv) can be controlled bythe same controller. At least two of (i) to (iv) can be controlled bydifferent controllers. The target surface can be an exposed surface of amaterial bed. The exposed surface can be planarized by a layerdispensing mechanism comprising a cyclonic separator. Thepre-transformed material can comprise at least one member of the groupconsisting of an elemental metal, metal alloy, ceramic, an allotrope ofelemental carbon, and an organic material. The pre-transformed materialcan comprise at least one member of the group consisting of an elementalmetal, metal alloy, ceramic, and an allotrope of elemental carbon. Thepre-transformed material can comprise a particulate material. Theparticulate material can comprise a powder material. Separate cancomprise become gas-borne, evaporate, or form plasma. The position cancomprise an area occupied by a footprint of the energy beam on thetarget surface, or a position adjacent to the area occupied by thefootprint. Adjacent is in an area having a radius of at most about sixfundamental length scales of the footprint that centers at thefootprint. The at least a portion can comprise a melt pool. Alter cancomprise reduce. Alter can comprise increase. The fraction thatseparated subsequently may form debris. The debris can comprise soot.The target surface is disposed in an enclosure. The fraction thatseparated may further react with one or more gasses in the enclosure.The one or more gasses can comprise oxygen or water. React can comprisechemically react. Chemically reacts can comprise oxidize. The debris canaffect the transforms a pre-transformed material into a transformedmaterial. Controlling can comprise using a processor. Controlling cancomprise a computer model of a physical process of the 3D printing. Thecomputer model may estimate a physical parameter of the physical processof the 3D printing. The target temperature value can be less than (I) attemperature at which the fraction separates (e.g., parts) from thetarget surface, (II) an evaporation temperature of the material type,(III) a plasma forming temperature of the material type, or (IV) anycombination thereof The at least one characteristic of the energy beamcan comprise dwell time, footprint, cross section, power per unit area,translation speed, focus, fluence, flux, or intensity.

In another aspect, a system for 3D printing of at least one 3D objectcomprises: (e.g., an enclosure configured to contain) a material bedincluding a pre-transformed material that comprises a material type; anenergy source that is configured to generate an energy beam that isconfigured to transform at least a portion of the pre-transformedmaterial into a transformed material as part of the 3D object, whichenergy beam optionally causes the at least a portion of the materialtype to part from the material bed; a detector that is configured todetect a temperature of the material bed; and at least one controlleroperatively coupled to the material bed, energy source, and detector,and is programmed to: (i) direct the energy beam to irradiate the atleast a portion of the pre-transformed material; (ii) direct thedetector to detect a temperature at a position of the material bed;(iii) evaluate a deviation between the temperature at the position and atarget temperature; and (iv) control at least one characteristic of theenergy beam to alter an amount of the material type that parted from thematerial bed using the evaluate.

The detector may be operatively coupled to the material bed. Thematerial bed may comprise an exposed surface. The exposed surface mayhave an average or mean planarity. The material type may comprise anelement. The material type may comprise an elemental metal, metal alloy,ceramic or an allotrope of elemental carbon. The material type maycomprise a polymer. The material type may comprise an organic material.The pre-transformed material may comprise a particulate material. Theparticulate material may comprise a powder material. The material typepart from the material bed can be evaporate and/or form plasma. Theposition of the material bed may comprise a position adjacent to the atleast a portion. The adjacent may comprise one or more FLS multipliersof the at least a portion. The at least a portion may comprise a meltpool. Alter may comprise reduce. Alter may comprise increase. The amountof the material type that parted from the material bed may subsequentlyform debris. The material bed may be disposed within an enclosure andthe amount of the material type that parted from the material bed mayfurther react with one or more gasses in the enclosure. The one or moregasses may comprise oxygen or water. Reacted may comprise chemicallyreacted. Chemically reacted may comprise oxidized. The debris maycomprise soot. Alter may comprise substantially eliminate. Substantiallymay be relative to the intended operation of the energy beam. The debrismay affect the transforms at least a portion of the pre-transformedmaterial into a transformed material. Alter may comprise (e.g.,substantially) reducing the amount of debris. Alter may comprise (e.g.,substantially) eliminating the debris. Substantial may be relative tothe affects the transforms at least a portion of the pre-transformedmaterial into a transformed material. Controlling may comprise using aprocessor. The system may further comprise a computer model of aphysical process of the 3D printing. The computer model may estimate aphysical parameter of the physical process of the 3D printing. Thetarget temperature may be less than a temperature at which the materialtype parts from the material bed. The target temperature may be lessthan an evaporation temperature of the material type. The targettemperature may be less than a plasma forming temperature of thematerial type. The characteristics of the energy beam may comprise dwelltime, footprint, cross section, power per unit area, translation speed,focus, fluence, flux, or intensity.

In another aspect, an apparatus for 3D printing of at least one 3Dobject comprises at least one controller that is programmed to: (a)direct generation of a material bed including a pre-transformed materialthat comprises a material type; (b) direct an energy source thatgenerates an energy beam that transforms at least a portion of thepre-transformed material into a transformed material as part of the 3Dobject, which energy beam optionally causes the at least a portion ofthe material type to part from the material bed; (c) direct the energybeam to irradiate at least a portion of the pre-transformed material andtransform the pre-transformed material to a transformed material as partof the 3D object; (d) direct a detector to detect a temperature at aposition of the material bed; (e) evaluate a deviation between thetemperature at the position and a target temperature; and (f) control atleast one characteristic of the energy beam to alter an amount of thematerial type that parted from the material bed using the evaluate,wherein the at least one controller is operatively coupled to thematerial bed, the detector, and to the energy source. At least two ofthe at least one controller programed to perform (a) to (f) may bedifferent controllers. At least two of (a) to (f) may be performed bythe same controller. The at least one controller may be a plurality ofcontrollers. The material bed may comprise an exposed surface. Theexposed surface may have an average or mean planarity. The material typemay comprise an element. The material type may comprise an elementalmetal, metal alloy, ceramic or an allotrope of elemental carbon. Thematerial type may comprise a polymer. The material type may comprise anorganic material. The pre-transformed material may comprise aparticulate material. The particulate material may comprise a powdermaterial. The material type part from the material bed can evaporateand/or form plasma. The position of the material bed may comprise aposition adjacent to the at least a portion. The adjacent may compriseone or more FLS multipliers of the at least a portion. The at least aportion may comprise a melt pool. Alter may comprise reduce. Alter maycomprise increase. The amount of the material type that parted from thematerial bed may (e.g., subsequently) form debris. The material bed maybe disposed within an enclosure and the amount of the material type thatparted from the material bed may further react with one or more gassesin the enclosure. The one or more gasses may comprise oxygen or water.Reacted may comprise chemically reacted. Chemically reacted may compriseoxidized. The debris may comprise soot. Alter may comprise reducing(e.g., substantially eliminating, wherein substantially may be relativeto the intended operation of the energy beam). The debris may affect thetransformation of at least a portion of the pre-transformed materialinto a transformed material. Alter may comprise reducing the debris(e.g., substantially eliminating the debris, wherein substantial may berelative to the affects the transforms at least a portion of thepre-transformed material into a transformed material). Controlling maycomprise using a processor. The apparatus may further comprise acomputer model of a physical process of the 3D printing. The computermodel may estimate a physical parameter of the physical process of the3D printing. The target temperature may be less than a temperature atwhich the material type parts from the material bed. The targettemperature may be less than an evaporation temperature of the materialtype. The target temperature may be less than a plasma formingtemperature of the material type. The characteristics of the energy beammay comprise dwell time, footprint, cross section, power per unit area,translation speed, focus, fluence, flux, or intensity.

The controller (e.g., of he at least one controller) may comprise aprocessor. The controller may comprise aproportional-integral-derivative (PID) controller. The controller maycomprise a nested controller. The controller may be programmed toperform closed loop control. The controller may be programmed to performopen loop control. The controller may comprise feedback control. Thecontroller may comprise feed forward control. The PID controller maycomprise a temperature controller. The PID controller may comprise ametrological controller. The nested controller may comprise atemperature controller or a metrological controller. The nestedcontroller may comprise a first temperature controller or a secondtemperature controller. The nested controller may comprise a firstmetrological controller or a second metrological controller.

In another aspect, a method for irradiation control comprises:projecting an energy beam that transforms at least a portion of a targetsurface into a transformed material, which energy beam causes the atleast a portion of the material type to part from the target surface;detecting a temperature at a position of the target surface; evaluatinga deviation between the temperature at the position and a targettemperature value; and controlling at least one characteristic of theenergy beam to alter an amount of the material type that parted from thematerial bed, which controlling is using the evaluation. The positionmay be within a footprint of the energy beam on the target surface.Adjacent to the position may comprise an area having a radius equal toat most about six footprint FLS (e.g., diameters) measured from thecenter of the footprint.

In another aspect, a method for 3D printing of at least one 3D objectcomprises: (a) disposing a pre-transformed material above a platform;(b) directing an energy beam towards the pre-transformed material totransform the pre-transformed material into a transformed material thatyields at least a portion of the 3D object; (c) irradiating the at leasta portion of the 3D object with the energy beam at a position, whereinthe energy beam optionally causes a fraction of the transformed materialto separate from the at least a portion of the 3D object; (d) detectinga temperature at the position; (e) evaluating a deviation between thetemperature detected in (d) at the position and a target temperatureprofile; and (f) controlling at least one characteristic of the energybeam using the evaluating, to alter an amount of the fraction that partsfrom the at least a portion of the 3D object.

In operation (f), the at least one characteristic of the energy beam canbe controlled to substantially eliminate or prevent the fraction fromseparating from the at least a portion of the 3D object. Substantiallycan be relative to the intended operation of the energy beam.Substantially can be relative to the affects the transforms at least aportion of the pre-transformed material into a transformed material. Thetarget surface can be an exposed surface of a material bed. The methodmay further comprise planarizing the exposed surface by using a layerdispensing mechanism that includes a cyclonic separator. Thepre-transformed material can comprise at least one member of the groupconsisting of an elemental metal, metal alloy, ceramic, an allotrope ofelemental carbon, and an organic material. The pre-transformed materialcan comprise at least one member of the group consisting of an elementalmetal, metal alloy, ceramic, and an allotrope of elemental carbon. Thepre-transformed material can comprise a particulate material. Theparticulate material can comprise a powder material. Separates cancomprise become gas-borne, evaporate or form plasma. The position cancomprise an area occupied by a footprint of the energy beam on thetarget surface, or a position adjacent to the area occupied by thefootprint, wherein adjacent can be in an area having a radius of at mostabout six fundamental length scales of the footprint that centers at thefootprint. The at least a portion can comprise a melt pool. The altercomprise reduce. The alter comprise increase. The fraction thatseparated subsequently forms debris. The debris can comprise soot. Thetarget surface can be disposed in an enclosure, and wherein the fractionthat separated further reacts with one or more gasses in the enclosure.The one or more gasses can comprise oxygen or water. Reacts can comprisechemically reacts. Chemically reacts can comprise oxidizes. The debriscan affect (e.g., in operation (a)) the transforms a pre-transformedmaterial into a transformed material. The target temperature value canbe less than (I) a temperature at which the fraction separates from thetarget surface, (II) an evaporation temperature of the material type,(III) a plasma forming temperature of the material type, or (IV) anycombination thereof The at least one characteristic of the energy beamcan comprise dwell time, footprint, cross section, power per unit area,translation speed, focus, fluence, flux, or intensity.

In another aspect, a method for 3D printing of at least one 3D objectcomprises: (a) disposing a pre-transformed material that comprises amaterial type in an enclosure to form a material bed; (b) projecting anenergy beam that transforms at least a portion of the pre-transformedmaterial into a transformed material as part of the 3D object, whichenergy beam optionally causes the at least a portion of the materialtype to part from the material bed; (c) directing the energy beam toirradiate at least a portion of the pre-transformed material andtransform the pre-transformed material to a transformed material as partof the 3D object; (d) detecting a temperature at a position of thematerial bed; (e) evaluating a deviation between the temperature at theposition and a target temperature; and (f) controlling at least onecharacteristic of the energy beam to alter an amount of the materialtype that parted from the material bed, which controlling is using theevaluation.

The material bed may comprise an exposed surface. The exposed surfacemay have an average or mean planarity. The material type may comprise anelement. The material type may comprise an elemental metal, metal alloy,ceramic or an allotrope of elemental carbon. The material type maycomprise a polymer. The material type may comprise an organic material.The pre-transformed material may comprise a particulate material. Theparticulate material may comprise a powder material. The material typepart from the material bed can be evaporate or form plasma. The positionof the material bed may comprise a position adjacent to the at least aportion. Adjacent may comprise one or more FLS multipliers of the atleast a portion. The at least a portion may comprise a melt pool. Altermay comprise reduce. Alter may comprise increase. The amount of thematerial type that parted from the material bed may subsequently formdebris. The material bed may be disposed within an enclosure and theamount of the material type that parted from the material bed mayfurther react with one or more gasses in the enclosure. The one or moregasses may comprise oxygen or water. Reacted may comprise chemicallyreacted. Chemically reacted may comprise oxidized. The debris maycomprise soot. Alter may comprise reduce (e.g., substantially eliminatewherein substantially may be relative to the intended operation of theenergy beam). The debris may affect the transforms at least a portion ofthe pre-transformed material into a transformed material. Alter maycomprise reducing (e.g., substantially eliminating) the debris, whereinsubstantial may be relative to the affects the transforms at least aportion of the pre-transformed material into a transformed material.Controlling may comprise using at least one processor. A computer modelof a physical process of the 3D printing may estimate at least onephysical parameter of the physical process of the 3D printing. Thetarget temperature may be less than a temperature at which the materialtype parts from the material bed. The target temperature may be lessthan an evaporation temperature of the material type. The targettemperature may be less than a plasma forming temperature of thematerial type. The characteristics of the energy beam may comprise dwelltime, footprint (e.g., on the exposed surface of the material bed),cross section, power per unit area, translation speed, focus, fluence,flux, or intensity.

In another aspect, a method for generating a multi layered (e.g., 3D)object (from a physical model) comprises: (a) transforming at least aportion of a pre-transformed material (e.g., that forms a material bed)to a transformed material with an energy beam to form a portion of themulti layered object; (b) measuring a physical property at a position onthe material bed, which position is adjacent to the portion of the multilayered object; (c) evaluating a deviation of the measured value of thephysical property from a target value, which target value is obtainedfrom a physical model (of the 3D object); and (d) controlling at leastone characteristic of the energy beam to achieve the target value of thephysical property, wherein controlling is using the evaluation.

The physical model may be an analogous model. The analogous model maycomprise an electrical model. The analogous model may comprise anelectronic model. The analogous model may comprise an electric circuit.The analogous model may comprise a resistor. The analogous model maycomprise a capacitor. The analogous model may comprise a ground element.The analogous model may comprise a current source. The analogous modelmay comprise a voltage element. The analogous model may comprise anelectrical branch. The electrical branch may comprise a resistor coupled(e.g., in parallel) to a capacitor. The electrical branch may representa physical property of at least a portion of the multi-layered (e.g.,3D) object. The physical property may comprise a heat profile over timeof (i) the energy beam (ii) the forming multi layered object, and/or(iii) the material bed. The physical property may comprise thermalhistory of (i) the energy beam (ii) the forming multi layered object,and/or (iii) the material bed. The physical property may comprise powerprofile over time of (i) the energy beam, (ii) the forming multi layeredobject, and/or (iii) the material bed. The physical property maycomprise dwell time sequence of (i) the energy beam (ii) the formingmulti layered object, and/or (iii) the material bed. The forming multilayered object (e.g., 3D object) may comprise the previously formedportion of the multi layered object. The electrical model electronically(e.g., substantially) imitates a physical property that affects theprinting of the 3D object. The pre-transformed material can for (or bepart of) a material bed. The material bed can be planarized using anapparatus comprising a cyclonic separator. The transforming can beduring a directing of the pre-transformed material to a platform. Thepre-transformed material can comprise a liquid, solid, or semi-solid.The pre-transformed material can comprise a particulate material. Theparticulate material can be selected from at least one member of thegroup consisting of elemental metal, metal alloy, ceramic, and anallotrope of elemental carbon. The physical property may be a physicalattribute.

In another aspect, a system for forming at least one 3D objectcomprises: a platform disposed in an enclosure; an energy source that isconfigured to provide an energy beam that transforms a pre-transformedmaterial to a transformed material, which energy beam is directedtowards the platform, and which energy source is operatively coupled tothe platform; a detector configured to detect a physical property of thetransformed material, which detector is operatively coupled to theplatform; and a controller operatively coupled to the energy source, anddetector, wherein the controller is programmed to (i) direct the energybeam to transform at least a portion of a pre-transformed material to atransformed material to form a portion of the three-dimensional object;(ii) direct the detector to measure a physical property at a positionthat is at or adjacent to the portion of the 3D object; (iii) evaluate adeviation of the measured value of the physical property from a targetvalue, which target value is obtained from a physical-model of the 3Dobject that comprises an electrical model; and (iv) use the evaluate in(iii) to control at least one characteristic of the energy beam toachieve the target value of the physical property.

The physical-model can be adjusted in real time during the forming ofthe at least one 3D object. Real time can be during a dwell time of theenergy beam along a hatch line forming a melt pool. The controller cancomprise a closed loop, open loop, feed forward, or feedback control.The physical-model can comprise one or more free parameters that areoptimized in real time during the forming of the at least one 3D object.The controller can comprise an internal-state-model that provides anestimate of an internal state of the forming of the at least one 3Dobject. The internal state can be derived from one or more measurementscomprising a measurement of the control variable or a measurement of theinput parameters. The internal-state-model can comprise astate-observer. The controller can comprise a graphical processing unit(GPU), system-on-chip (SOC), application specific integrated circuit(ASIC), application specific instruction-set processor (ASIPs),programmable logic device (PLD), or field programmable gate array(FPGA). The electrical component can comprise an active, passive, orelectromechanical components. The electromechanical component cancomprise a piezoelectric device, crystal, resonator, terminal,connector, cable assembly, switch, protection device, mechanicalaccessory, printed circuit board, memristor, or a waveguide. Theelectronic component can comprise a variable or non-variable component.The electronic component may not be a variable. The control-model cancomprise a plurality of electrical components. The control-model cancomprise a software (e.g., a non-transitory computer-readable medium inwhich program instructions are stored) that simulates and/or imitatesthe operation of a plurality of electrical components. Thepre-transformed material may be at least a portion of a material bed.The material bed may be planarized using layer dispensing mechanismcomprising a cyclonic separator. The transforming can be during adirecting of the pre-transformed material to a platform. Thepre-transformed material may comprise a liquid, solid, or semi-solid.The pre-transformed material may comprise a particulate material. Theparticulate material can be selected from at least one member of thegroup consisting of elemental metal, metal alloy, ceramic, and anallotrope of elemental carbon.

In another aspect, a system for forming at least one 3D object,comprises: (a) an energy beam that transforms a pre-transformed material(e.g., that is at least a portion of a material bed) to a transformedmaterial; and (b) a controller comprising a control-model that isrelated to a requested 3D object, which control-model is configured inthe controller, which controller is operative coupled to the energy beamand is programmed to direct the energy beam to transform thepre-transformed material (e.g., that is at least a portion of thematerial bed) to form the at least one 3D object using the control-modelthe control-model comprises an electronic element.

The control-model may be adjusted in real time during the forming of theat least one 3D object. Real time may be during a dwell time of theenergy beam along a hatch line forming a melt pool. The parameter maycomprise a temperature, height, or power density. The at least one 3Dobject may be a plurality of 3D objects. The plurality of 3D objects maybe formed in the same material bed. The plurality of 3D objects may beformed in parallel. The controller may comprise a closed loop or openloop control. The controller may comprise a feedback or feed-forwardcontrol. The control-model may comprise one or more free parameters thatare optimized in real time during the forming of the at least one 3Dobject. The controller may comprise an internal-state-system (e.g.,internal-state-model) that provides an estimate of an internal state ofthe forming of the at least one 3D object. The internal state may bederived from one or more measurements comprising a measurement of thecontrol variable or a measurement of the input parameters. Theinternal-state-system may comprise a state-observer. The control-modelmay comprise a state-observer-model. The controller may comprise agraphical processing unit (GPU), system-on-chip (SOC), applicationspecific integrated circuit (ASIC), application specific instruction-setprocessor (ASIPs), programmable logic device (PLD), or fieldprogrammable gate array (FPGA). The (at least one) 3D object may besubstantially similar to the requested (at least one) 3D object.Substantially may be relative to the intended purpose of the (at leastone) 3D object. The electrical component may comprise an active,passive, or electromechanical components. The active component maycomprise a diode, transistor, integrated circuit, optoelectronic device,display device, vacuum tube, discharge device, or a power source. Thepassive component may comprise a resistor, capacitor, magnetic device,memristor, network, transducer, sensor, detector, antenna, oscillator,display device, filter, wire-wrap, or a breadboard. Theelectromechanical component may comprise a mechanical accessory, printedcircuit board, or a memristor. The electronic component may be variable.The electronic component may not be variable. The control-model maycomprise a plurality of electrical components. The control-model mayelectronically imitate substantially a physical property that affectsthe forming 3D object. Substantially may be relative to the intendedpurpose of the 3D object.

In another aspect, a system for 3D printing of at least one 3D object,comprises: (a) an energy beam that transforms a pre-transformed materialto a transformed material; and (b) a controller comprising acomputer-model that is related to a requested 3D object, whichcontroller is operative coupled to the energy beam and is programmed todirect the energy beam to transform the pre-transformed material to atransformed material using the computer-model, which computer-modelcomprises an electronic element that imitates at least a portion of the3D printing.

The computer-model comprising the electronic element may evolve duringthe 3D printing. Evolve may be in real-time. Real-time may compriseduring formation of the 3D object. Real-time may comprise duringformation of a layer of the 3D object. Real-time may comprise during ahatch line forming the layer of the 3D object. Real-time may be during apath along which the energy beam propagates to form the layer of the 3Dobject. Real-time may be during formation of at most two successive meltpools as part of the 3D object. Real time may be during formation of atmost one melt pool as part of the 3D object. The computer model maycomprise adaptive control. The computer model may comprise modelpredictive control. The computer model may evolve based on a time-spanrequired to reach a threshold value. The threshold value may be atemperature of a melt pool as part of the 3D object. The temperature ofthe melt pool may be measured from the exposed surface of the melt pool.The threshold value may be a temperature of a position at a vicinity ofthe melt pool. The vicinity may be at most five FLS of the melt pool.The position at the vicinity may be in an exposed surface of thematerial bed. The computer-model may comprise a plurality of electronicelements that together imitate at least a portion of the 3D printing ofat least a portion of the 3D object. The computer model may comprise anarchitecture of the plurality of electronic elements that imitates atleast a portion of the 3D printing of at least a portion of the 3Dobject. The imitation may comprise mechanical or thermal behavior of theat least a portion of the 3D object during its 3D printing. Themechanical behavior may comprise plastic or elastic behavior. Thecomputer-model may consider the material properties of the at least aportion of the 3D object. The control-model may be adjusted in real timeduring at least a portion of the 3D printing. Real time may be during adwell time of the energy beam (e.g., along a hatch line) forming a meltpool. The parameter may comprise a temperature, height, or powerdensity. The at least one 3D object may be a plurality of 3D objects.The plurality of 3D objects may be formed in the same material bed. Theplurality of 3D objects may be formed in parallel. The controller maycomprise a closed loop or open loop control. The controller may comprisea feedback or feed-forward control. The control-model may comprise oneor more free parameters that are optimized in real time during theforming of the at least one 3D object. The controller may comprise aninternal-state-system that provides an estimate of an internal state ofthe forming of the at least one 3D object. The control may compriseadaptive control. The control may comprise model predictive control. Thecontrol algorithm may evolve in real-time during the 3D printing.Real-time may be during formation of a layer of the 3D object. Theinternal state may be derived from one or more measurements comprising ameasurement of the control variable or a measurement of the inputparameters. The internal-state-system may comprise a state-observer. Thecontrol-model may comprise a state-observer-model. The controller maycomprise a graphical processing unit (GPU), system-on-chip (SOC),application specific integrated circuit (ASIC), application specificinstruction-set processor (ASIPs), programmable logic device (PLD), orfield programmable gate array (FPGA). The 3D object may be (e.g.,substantially) similar to the requested 3D object. Substantially may berelative to the intended purpose of the 3D object. The electricalcomponent may comprise an active, passive, or electromechanicalcomponents. The active component may comprise a diode, transistor,integrated circuit, optoelectronic device, display device, vacuum tube,discharge device, or a power source. The passive component may comprisea resistor, capacitor, magnetic device, memristor, network, transducer,sensor, detector, antenna, oscillator, display device, filter,wire-wrap, or a breadboard. The electromechanical component may comprisea mechanical accessory, printed circuit board, or a memristor. Theelectronic component may be variable. The electronic component may notbe variable. The control-model may comprise a plurality of electricalcomponents. The control-model may electronically imitate substantially aphysical property that affects the forming 3D object. Substantially maybe relative to the intended purpose of the 3D object.

In another aspect, a method for forming a 3D object, comprises: (a)transforming a portion of a material bed with an energy beam to form atleast a portion of the 3D object; and (b) controlling (e.g., in realtime) at least one characteristic of the energy beam with a controllercomprising a control-model related to a requested 3D object, whichcontrol-model is configured in the controller, wherein the 3D object issubstantially similar to the requested 3D object, wherein thecontrol-model comprises an electrical component.

The control-model may be adjusted in real time during the forming of the3D object. Real time may be during a dwell time of the energy beam(e.g., along a hatch line) forming a melt pool. The controlling may usea processor comprising at least 3 Tera floating point operations persecond, according to a benchmark. Transforming a portion of a materialbed with an energy beam to form at least a portion of the 3D object andcontrolling in real time at least one characteristic of the energy beamwith a controller comprising a control-model related to a requested 3Dobject, may be repeated after adjusting the at least one characteristicof the energy beam. The closed loop control may use at least onethreshold value. The control-model may comprise a simplified modelrelative to the requested model of the 3D object. Substantially may berelative to the intended purpose of the 3D object. The control-model maycomprise a state-observer-model. The control-model may comprise asimulation. The simulation may comprise a temperature or a mechanicalsimulation of the 3D printing (e.g., of the respective behavior of theforming 3D object during its 3D printing). The simulation may comprise amaterial property of the 3D object. The simulation may comprise ageometry of the 3D object. The physical model, control-model, and/orcomputer model may be dynamically adjusted in the real time during theforming of the 3D object (e.g., during the irradiation of the energybeam). The electrical component may comprise an active, passive, orelectromechanical components. The active component may comprise a diode,transistor, integrated circuit, optoelectronic device, display device,vacuum tube, discharge device, or a power source. The passive componentmay comprise a resistor, capacitor, magnetic device, memristor, network,transducer, sensor, detector, antenna, oscillator, display device,filter, wire-wrap, or a breadboard. The electromechanical component maycomprise a mechanical accessory, printed circuit board, or a memristor.The electronic component may be variable. The electronic component maynot be variable. The physical-model may comprise a plurality ofelectrical components. The physical-model may electronically (e.g.,substantially) imitate a physical property that affects the forming 3Dobject. Substantially may be relative to the intended purpose of the 3Dobject.

In another aspect, an apparatus for forming a 3D object comprises atleast one controller that is programmed to (a) direct an energy beam totransform a portion of a material bed to form at least a portion of the3D object; and (b) control (e.g., in real time) at least onecharacteristic of the energy beam, wherein the controller comprises acomputer -model related to a requested 3D object, which computer-modelis configured in the controller, wherein the 3D object is substantiallysimilar to the requested 3D object, wherein the computer-model comprisesan electrical component. Operations (a) and (b) may be directed by thesame controller. Operations (a) and (b) may be directed by differentcontrollers (e.g., that are operatively coupled to one another). Thecomputer-model may imitate and/or be analogous to a thermo-mechanicalmodel (e.g., of forming the 3D object).

In another aspect, a computer software product for forming at least onethree dimensional object comprises a non-transitory computer-readablemedium in which program instructions are stored, which instructions,when read by a computer, cause the computer to perform operationscomprising: (a) direct an energy beam to transform a portion of amaterial bed to form at least a portion of the 3D object; and (b) use acomputer model to control (e.g., in real time) at least onecharacteristic of the energy beam, which computer-model is related to arequested 3D object, which computer-model is operatively coupled to thecontroller, wherein the 3D object is substantially similar to therequested 3D object, wherein the computer-model comprises an electricalcomponent. The computer-model may imitate and/or be analogous to athermo-mechanical model (e.g., of forming the 3D object).

In another aspect, a method for estimating a fundamental length scale ofa melt pool comprises: directing to a target surface an energy beam thatis spatially oscillating by a spatial amplitude of at most about 50percent of the energy beam footprint on the target surface; and duringthe oscillating: (a) using temperature values to estimate thefundamental length scale, comprising: (I) holding a power of an energysource that generates the energy beam at a constant value or at asubstantially constant value; (II) measuring (e.g., in real time) afirst temperature of a position at the target surface that coincideswith the footprint as it oscillates, and collecting the temperaturevalues by repeating the measuring over time until a melt pool is formedat the target surface; and (III) deriving the fundamental length scaleof the melt pool by using an average minimum of the temperature values,and an average maximum of the temperature values; or (b) using powervalues to estimate the fundamental length scale, comprising: (i)controlling (e.g., in real-time) a second temperature at a constanttemperature value, which second temperature is of a position of thetarget surface that coincides with the footprint as it oscillates; (ii)measuring (e.g., in real-time) the power of an energy source thatgenerates the energy beam, and collecting power values by repeating themeasuring over time until a melt pool is formed at the target surface;and (iii) deriving the fundamental length scale of the melt pool from anaverage minimum value of the measured power, and a maximum values of themeasured power.

The target surface can be an exposed surface of the material bed. Thematerial bed may comprise a particulate material. The particulatematerial can comprise powder. The material bed can comprise at least onematerial selected from the group consisting of elemental metal, metalalloy, ceramics, and an allotrope of elemental carbon. Transforming cancomprise melting or sintering. Melting can comprise complete melting.The movement can be at most about 10 percent of the fundamental lengthscale of the footprint. The energy beam can comprise a laser beam or anelectron beam. The energy beam can comprise a laser beam. The energysource can comprise a laser or an electron gun. The energy source cancomprise a laser. In real time comprises during formation of the meltpool. The control can comprise closed loop control or feedback control.The using can comprise subtracting the average maximum of thetemperature values from the average maximum of the temperature values.The using can comprise subtracting the average maximum of the powervalues from the average minimum of the temperature values. The energybeam can be oscillating by a spatial amplitude of at most about 30percent of a footprint of the energy beam on the target surface. Theenergy beam can be oscillating by a spatial amplitude of at most about20 percent of a footprint of the energy beam on the target surface. Theenergy beam can be oscillating by a spatial amplitude of at most about10 percent of a footprint of the energy beam on the target surface.Substantially constant value in (a) is relative to inducing a negligentor undetectable effect on the measured temperature. Substantiallyconstant value in (b) is relative to a negligent effect on a detectablepower variation. Comprising in (III) considering the footprint positionthat is associated with the temperature value. Comprising in (III)considering the footprint position that is associated with the powervalue. Spatially oscillating can be a back and forth movement along adirection. The direction can be of a forming a line (e.g., file) of meltpools. At least two of the melt pools may overlap at least in part. Thefundamental length scale may comprise a diameter or diameter equivalent.

In another aspect, a system for estimating a fundamental length scale ofa melt pool comprises: a target surface; an energy source configured togenerate an oscillating energy beam that irradiates the target surface,which cross section of the energy beam on the target surface is afootprint of the energy beam, which energy beam is configured totransform the target surface to form a melt pool, which energy beam isconfigured to spatially oscillate by a spatial amplitude of at mostabout 50 percent of the energy beam footprint on the target surface,wherein the energy source is operatively coupled to the target surface;a sensor comprising: (A) a power sensor configured to detect the powerof the energy source, or (B) a temperature sensor configured to detect atemperature at a position of the footprint at the target surface,wherein the sensor is operatively coupled to the target surface; and atleast one controller that is operatively coupled to the energy source,and to the energy beam, and is programmed to: direct the spatiallyoscillating energy beam to the target surface and estimate fundamentallength scale, comprising: (a) (I) control operation of the power sourceat a constant value or at a substantially constant value, (II) directmeasurement (e.g., in real time) of a first temperature of a position atthe target surface that coincides with the footprint as it oscillates,and direct collection of temperature values by repeating the measurementover time until a melt pool is formed at the target surface by theoscillating energy beam; and (III) direct derivation of the fundamentallength scale of the melt pool by using an average minimum of thetemperature values, and an average maximum of the temperature values; or(b) (i) control (e.g., in real-time) a second temperature at a constanttemperature value, which second temperature is of a position of thetarget surface that coincides with the footprint as it oscillates; (ii)direct measurement (e.g., in real-time) of a power value of the energysource, and direct collection of power values by repeating themeasurement over time until a melt pool is formed at the target surface;and (iii) direct derivation of the fundamental length scale of the meltpool from an average minimum value of the measured power, and a maximumvalues of the measured power. At least two of (I) to (III) can bedirected by the same controller. At least two of (I) to (III) can bedirected by the different controllers. At least two of (i) to (iii) canbe directed by the same controller. At least two of (i) to (iii) can bedirected by the different controllers. At least one controller comprisesclosed loop control or feedback control. The target surface may bedisposed in an enclosure.

In another aspect, an apparatus for estimating a fundamental lengthscale of a melt pool comprises at least one controller that isoperatively coupled to (A) an energy source that is configured togenerate an energy beam, and to (B) the energy beam that is configuredto irradiate and transform a portion of a target surface to form a meltpool, which energy beam is configured to oscillate by a spatialamplitude of at most about 50 percent of the energy beam footprint onthe target surface, which at least one controller is programmed to:direct the energy beam to the target surface and estimate thefundamental length scale of the melt pool, comprising: (a) (I) controlan operation of the power source at a constant power value or at asubstantially constant power value, (II) direct measurement (e.g., inreal time) of a first temperature of a position at the target surfacethat coincides with the footprint as it oscillates, and directcollection of temperature values by repeating the measurement over timeuntil a melt pool is formed at the target surface by the oscillatingenergy beam; and (III) direct derivation of the fundamental length scaleof the melt pool by using an average minimum of the temperature values,and an average maximum of the temperature values; or (b) (i) control(e.g., in real-time) a second temperature at a constant temperaturevalue, which second temperature is of a position of the target surfacethat coincides with the footprint as it oscillates; (ii) directmeasurement (e.g., in real-time)of a power value of the energy source,and direct collection of power values by repeating the measurement overtime until a melt pool is formed at the target surface; and (iii) directderivation of the fundamental length scale of the melt pool from anaverage minimum value of the measured power, and a maximum values of themeasured power. At least two of (I) to (III) can be directed by the samecontroller. At least two of (I) to (III) can be directed by thedifferent controllers. At least two of (i) to (iii) can be directed bythe same controller. At least two of (i) to (iii) can be directed by thedifferent controllers. At least one controller can comprise closed loopcontrol or feedback control. At least one controller can comprise openloop control or feed forward control.

In another aspect, a computer software product for estimating afundamental length scale of a melt pool comprises a non-transitorycomputer-readable medium in which program instructions are stored, whichinstructions, when read by a computer, cause the computer to performoperations comprising: (a) derive the fundamental length scale of themelt pool by using an average minimum of temperature values, and anaverage maximum of the temperature values, wherein the temperaturevalues are of positions at the target surface that coincide withfootprints of a first energy beam that irradiates the target surface andspatially oscillates by a spatial amplitude of at most about 50 percentof the footprint on the target surface, which energy beam is generatedby an energy source that is held at a constant or substantially constantpower value; or (b) derive the fundamental length scale of the melt poolby using an average minimum of power values, and an average maximum ofthe power values, wherein the power values are of a second energy sourcethat generates a second energy beam that irradiates the target surface,wherein the temperature at a position at the target surface thatcoincides with the footprint, is controlled to be at a constanttemperature value, or at a substantially constant temperature value.

Another aspect of the present disclosure provides a non-transitorycomputer-readable medium comprising machine-executable code that, uponexecution by one or more computer processors, implements any of themethods above or elsewhere herein.

Another aspect of the present disclosure provides a computer systemcomprising one or more computer processors and a non-transitorycomputer-readable medium coupled thereto. The non-transitorycomputer-readable medium comprises machine-executable code that, uponexecution by the one or more computer processors, implements any of themethods above or elsewhere herein.

Additional aspects and advantages of the present disclosure will becomereadily apparent to those skilled in this art from the followingdetailed description, wherein only illustrative embodiments of thepresent disclosure are shown and described. As will be realized, thepresent disclosure is capable of other and different embodiments, andits several details are capable of modifications in various obviousrespects, all without departing from the disclosure. Accordingly, thedrawings and description are to be regarded as illustrative in nature,and not as restrictive.

INCORPORATION BY REFERENCE

All publications, patents, and patent applications mentioned in thisspecification are herein incorporated by reference to the same extent asif each individual publication, patent, or patent application wasspecifically and individually indicated to be incorporated by reference.

BRIEF DESCRIPTION OF DRAWINGS

The novel features of the invention are set forth with particularity inthe appended claims. A better understanding of the features andadvantages of the present invention will be obtained by reference to thefollowing detailed description that sets forth illustrative embodiments,in which the principles of the invention are utilized, and theaccompanying drawings or figures (also “FIG.” and “FIGs.” herein), ofwhich:

FIG. 1 shows a schematic side view of a 3D printing system andapparatuses;

FIG. 2 schematically illustrates an optical system;

FIG. 3 shows a schematic side view of a 3D printing system andapparatuses;

FIG. 4 shows a schematic side view of a 3D printing system andapparatuses;

FIG. 5 shows a schematic side view of a 3D printing system andapparatuses;

FIG. 6 shows a schematic views of 3D objects;

FIG. 7 shows schematics of various vertical cross sectional views ofdifferent 3D objects;

FIG. 8 shows a horizontal view of a 3D object;

FIG. 9 schematically illustrates a coordinate system;

FIGS. 10A-10C shows various 3D objects and schemes thereof;

FIG. 11 schematically illustrates a computer control system that isprogrammed or otherwise configured to facilitate the formation of one ormore 3D objects;

FIG. 12 illustrates a path;

FIG. 13 illustrates various paths;

FIG. 14 illustrates a schematic side view (as a vertical crosssectional) of a 3D printing system portion;

FIG. 15 illustrates a schematic side view (as a vertical crosssectional) of a 3D printing system portion;

FIG. 16 illustrates a schematic side view (e.g., vertical crosssectional) of a 3D printing system portion;

FIG. 17 shows schematics of various vertical cross sectional views ofdifferent 3D objects;

FIG. 18 shows a schematic representation of a 3D object;

FIG. 19 shows an exposed surface of a material bed;

FIG. 20 shows a representation of a control scheme;

FIGS. 21A-21D show various schematic representations of intensity as afunction of time;

FIGS. 22A-22D show various schematic representations ofphysical-attribute profiles as a function of time;

FIGS. 23A-23B show schematics 3D objects in material beds;

FIG. 24 schematically illustrates a control system used in the formationof one or more 3D objects;

FIG. 25 schematically illustrates a control system that is programmed orotherwise configured to facilitate debris reduction (e.g., avoidance)during formation of one or more 3D objects;

FIGS. 26A-26B show schematic representations of a material bed;

FIGS. 27A-27B schematically illustrate various physical models;

FIGS. 28A-28D show various schematic representations of measuredphysical profiles over times;

FIG. 29 shows a schematic side view of a 3D printing system andapparatuses;

FIGS. 30A-30D schematically illustrate various steps in a 3D printingprocess; and FIG. 30E schematically illustrates a graph associated witha 3D printing process;

FIG. 31 shows a schematic top view of a layer of material;

FIGS. 32A-32D show various schematic representations of measuredphysical-attribute profiles as a function of time;

FIG. 33 shows a schematic side view of a 3D printing system andapparatuses;

FIG. 34 shows a cross section in a 3D object;

FIG. 35 shows a 3D object;

FIG. 36 schematically illustrates a cross section in portion of a 3Dobject; and

FIG. 37 schematically illustrates a vertical cross section in a portionof an optical detection system.

The figures and components therein may not be drawn to scale. Variouscomponents of the figures described herein may not be drawn to scale.Any dimensions in the various drawings are for illustrative purposesonly and are not intended to be limiting. Other dimensions andproportions not listed or visualized are contemplated and intended to beincluded within the scope of the invention.

DETAILED DESCRIPTION

While various embodiments of the invention have been shown and describedherein, it will be obvious to those skilled in the art that suchembodiments are provided by way of example only. Numerous variations,changes, and substitutions may occur to those skilled in the art withoutdeparting from the invention. It should be understood that variousalternatives to the embodiments of the invention described herein mightbe employed.

Terms such as “a,” “an” and “the” are not intended to refer to only asingular entity, but include the general class of which a specificexample may be used for illustration. The terminology herein is used todescribe specific embodiments of the invention, but their usage does notdelimit the invention.

When ranges are mentioned, the ranges are meant to be inclusive, unlessotherwise specified. For example, a range between value 1 and value 2 ismeant to be inclusive and include value 1 and value 2. The inclusiverange will span any value from about value 1 to about value 2. The term“between” as used herein is meant to be inclusive unless otherwisespecified. For example, between X and Y is understood herein to meanfrom X to Y. The term “adjacent” or “adjacent to,” as used herein,includes ‘next to,’ ‘adjoining,’ ‘in contact with,’ and ‘in proximityto.’ In some instances, adjacent to may be ‘above’ or ‘below.’

The term “operatively coupled” or “operatively connected” refers to afirst mechanism that is coupled (or connected) to a second mechanism toallow the intended operation of the second and/or first mechanism.

Three-dimensional printing (also “3D printing”) generally refers to aprocess for generating a 3D object. For example, 3D printing may referto sequential addition of material layer or joining of material layers(or parts of material layers) to form a 3D structure, in a controlledmanner. The controlled manner may include automated control. In the 3Dprinting process, the deposited material can be transformed (e.g.,fused, sintered, melted, bound, or otherwise connected) to (e.g.,subsequently) harden and form at least a part of the 3D object. Fusing(e.g., sintering or melting) binding, or otherwise connecting thematerial is collectively referred to herein as transforming thepre-transformed material (e.g., powder material). Fusing thepre-transformed material may include melting or sintering thepre-transformed material. Binding can comprise chemical bonding.Chemical bonding can comprise covalent bonding. Examples of 3D printingmay include additive printing (e.g., layer by layer printing, oradditive manufacturing). 3D printing may include layered manufacturing.3D printing may include rapid prototyping. 3D printing may include solidfreeform fabrication. 3D printing may include direct materialdeposition. The 3D printing may further comprise subtractive printing.

In some embodiments, the 3D object comprises a hanging structure. Thehanging structure may be a plane like structure (referred to herein as“three-dimensional plane,” or “3D plane”). The 3D plane may have arelatively small width as opposed to a relatively large surface area.For example, the 3D plane may have a small height relative to a largehorizontal projection (e.g., plane). The 3D plane may be planar, curved,or assume an amorphous 3D shape. The 3D plane may be a strip, a blade,or a ledge. The 3D plane may comprise a curvature. The 3D plane may becurved. The 3D plane may be planar (e.g., flat). The 3D plane may have ashape of a curving scarf. The 3D object may comprise a wire.

3D printing methodologies can comprise extrusion, wire, granular,laminated, light polymerization, orpowder-bed-and-inkjet-head-3D-printing. Extrusion 3D printing cancomprise robo-casting, fused deposition modeling (FDM) or fused filamentfabrication (FFF). Wire 3D printing can comprise electron beam freeformfabrication (EBF3). Granular 3D printing can comprise direct metal lasersintering (DMLS), electron beam melting (EBM), selective laser melting(SLM), selective heat sintering (SHS), or selective laser sintering(SLS). Powder bed and inkjet head 3D printing can comprise plaster-based3D printing (PP). Laminated 3D printing can comprise laminated objectmanufacturing (LOM). Light polymerized 3D printing can comprisestereo-lithography (SLA), digital light processing (DLP), or laminatedobject manufacturing (LOM). 3D printing methodologies can compriseDirect Material Deposition (DMD). The Direct Material Deposition maycomprise, Laser Metal Deposition (LMD, also known as, Laser depositionwelding). 3D printing methodologies can comprise powder feed, or wiredeposition.

3D printing methodologies may differ from methods traditionally used insemiconductor device fabrication (e.g., vapor deposition, etching,annealing, masking, or molecular beam epitaxy). In some instances, 3Dprinting may further comprise one or more printing methodologies thatare traditionally used in semiconductor device fabrication. 3D printingmethodologies can differ from vapor deposition methods such as chemicalvapor deposition, physical vapor deposition, or electrochemicaldeposition. In some instances, 3D printing may further include vapordeposition methods.

The methods, apparatuses, software, and systems of the presentdisclosure can be used to form 3D objects for various uses andapplications. Such uses and applications include, without limitation,electronics, components of electronics (e.g., casings), machines, partsof machines, tools, implants, prosthetics, fashion items, clothing,shoes, or jewelry. The implants may be directed (e.g., integrated) to ahard, a soft tissue, or to a combination of hard and soft tissues. Theimplants may form adhesion with hard and/or soft tissue. The machinesmay include a motor or motor part. The machines may include a vehicle.The machines may comprise aerospace related machines. The machines maycomprise airborne machines. The vehicle may include an airplane, drone,car, train, bicycle, boat, or shuttle (e.g., space shuttle). The machinemay include a satellite or a missile. The uses and applications mayinclude 3D objects relating to the industries and/or products listedherein.

The present disclosure provides systems, apparatuses, software, and/ormethods for 3D printing of a desired 3D object from a pre-transformedmaterial (e.g., powder material). Pre-transformed material as understoodherein is a material before it has been transformed by an energy beam(e.g., transforming energy beam) during the 3D printing process. Thepre-transformed material may be a material that was, or was not,transformed prior to its use in the 3D printing process. The object canbe pre-ordered, pre-designed, pre-modeled, or designed in real time(i.e., during the process of 3D printing). The 3D printing method can bean additive method in which a first layer of hardened material isprinted, and thereafter a volume of a pre-transformed material is addedto the first layer as separate sequential layer (or parts thereof). Eachadditional sequential layer (or part thereof) can be added to theprevious layer of hardened material by transforming (e.g., fusing (e.g.,melting)) a fraction of the pre-transformed material into a transformedmaterial. The transformed material may be a hardened material.Alternatively, the transformed material may subsequently harden (e.g., asolid powder may melt and subsequently solidify). The hardened layer maybe at least a portion of the (hard) 3D object. The hardening can beactively induced (e.g., by cooling) or can occur without intervention(i.e., naturally). The transformation of the pre-transformed materialmay be effectuated by using one or more energy beams. Thepre-transformed material may be disposed in a material bed prior to itstransformation (e.g., by the energy beam). At time, the pre-transformedmaterial is injected onto a platform and be transform before contactingthe platform (e.g., on its way to the platform), or just when contactingthe platform. The layer of pre-transformed material may be depositedusing a layer dispensing mechanism (e.g., comprising a materialdispensing mechanism, leveling mechanism, and/or a material removalmechanism). The temperature of the material bed (e.g., interior, and/orexposed surface thereof) may be controlled by a controller. Themetrological parameters of the material bed (e.g., exposed surfacethereof) may be controlled by a controller. The metrological parametersof the layer of hardened material (e.g., exposed surface thereof) may becontrolled by a controller. The metrological parameters of the 3D object(e.g., exposed surface thereof) may be controlled by a controller.Metrological parameters may comprise height, width, or length.In someembodiments, the 3D printing comprises heating at least a portion of amaterial bed, and/or a previously formed area of hardened material usingat least one transforming energy source. In some embodiments, the heatedarea may comprise an area of transformed material. The heated area mayencompass the bottom skin layer. The heated area may comprise a heataffected zone (e.g., FIG. 26A, 2610). The heated area may allow aparallel positon at the bottom skin layer to reach an elevatedtemperature that is above the solidus temperature (e.g., and at or belowthe liquidus temperature) of the material at the bottom skin layer,transform (e.g., sinter or melt), become liquidus, and/or plasticallyyield, which parallel position is parallel to the irradiated position atthe exposed surface. For example, the heated area may allow the layerscomprising the bottom skin layer to reach an elevated temperature thatis above the solidus temperature of the material (e.g., and at or belowthe liquidus temperature of the material at the previously formed layersuch as the bottom skin layer), transform, become liquidus, and/orplastically yield. The heating by the transforming energy beam may allowreaching an elevated temperature that is above the: solidus temperatureof the material (e.g., and at or below its liquidus temperature),transforming (e.g., melting) temperature, liquefying temperature,temperature of becoming liquidus, and/or plastic yielding temperature ofthe heated layer of hardened material and/or one or more layers beneaththe heated layer (e.g., the bottom skin layer). For example, the heatingmay penetrate one, two, three, four, five, six, seven, eight, nine, ten,or more layers of the hardened material (e.g., not only the layer thatis exposed, but also deeper layers within the 3D object), or the entire3D object (e.g., or unsupported portion thereof) reaching the bottomskin layer. For example, heating may penetrate one, two, three, four,five, six, seven, eight, nine, ten, or more layers of thepre-transformed material (e.g., not only the layer that is exposed inthe material bed, but also deeper layers within the material bed), orthe entire depth of the material bed (e.g., fuse the entire depth of thematerial bed).

The very first formed layer of hardened material in a 3D object isreferred to herein as the “bottom skin.” In some embodiments, the bottomskin layer is the very first layer in an unsupported portion of a 3Dobject. The unsupported portion may not be supported by auxiliarysupports. The unsupported portion may be connected to the center (e.g.,core) of the 3D object and may not be otherwise supported by, oranchored to, the platform. For example, the unsupported portion may be ahanging structure (e.g., a ledge) or a cavity ceiling.

In some embodiments, the 3D object comprises a first portion and asecond portion. The first portion may be connected to a sub-structure(e.g., core) at one, two, or three sides (e.g., as viewed from the top).The sub-structure may be the rest of the 3D object. The second portionmay be connected to the sub-structure at one, two, or three sides (e.g.,as viewed from the top). For example, the first and second portion maybe connected to a sub-structure (e.g., column, post, or wall) of the 3Dobject. For example, the first and second portion may be connected to anexternal cover that is a part of the 3D object. The first and/or secondportion may be a wire or a 3D plane. The first and/or second portion maybe different from a wire or 3D plane. The first and/or second portionmay be a blade (e.g., turbine or impeller blade). The first and secondportions may be (e.g., substantially) identical in terms of structure,geometry, volume, and/or material composition. The first and secondportions may be (e.g., substantially) identical in terms of structure,geometry, volume, material composition, or any combination thereof Thefirst portion may comprise a top surface. Top may be in the directionaway from the platform and/or opposite to the gravitational field. Thesecond portion may comprise a bottom surface (e.g., bottom skinsurface). Bottom may be in the direction towards the platform and/or inthe direction of the gravitational field. FIG. 36 shows an example of afirst (e.g., top) surface 3610 and a second (e.g., bottom) surface 3620.At least a portion of the first and second surfaces are separated by agap. At least a portion of the first surface is separated by at least aportion of the second surface (e.g., to constitute a gap). The gap maybe filled with pre-transformed or transformed (e.g., and subsequentlyhardened) material during the formation of the 3D object. The secondsurface may be a bottom skin layer. FIG. 36 shows an example of avertical gap distance 3640 that separates the first surface 3610 fromthe second surface 3620. The vertical gap distance may be equal to thedistance disclosed herein between two adjacent 3D planes. The verticalgap distance may be equal to the vertical distance of the gap asdisclosed herein. The vertical distance of the gap may be at least about30 μm, 35 μm, 40 μm, 50 μm, 60 μm, 70 μm, 80 μm, 90 μm, 100 μm, 150 μm,200 μm, 0.05 mm, 0.1 mm, 0.25 mm, 0.5 mm, 1 mm, 2 mm, 3 mm, 4 mm, 5 mm,6 mm, 7 mm, 8 mm, 9 mm, or 10 mm. The vertical distance of the gap maybe at most about 0.05 mm, 0.1 mm, 0.25 mm, 0.5 mm, 1 mm, 2 mm, 3 mm, 4mm, 5 mm, 6 mm, 7 mm, 8 mm, 9 mm, 10 mm, or 20 mm. The vertical distanceof the gap may be any value between the afore-mentioned values (e.g.,from about 30 μm to about 200 μm, from about 100 μm to about 200 μm,from about 30 μm to about 100 mm, from about 80 mm to about 150 mm, fromabout 0.05 mm to about 20 mm, from about 0.05 mm to about 0.5 mm, fromabout 0.2 mm to about 3 mm, from about 0.1 mm to about 10 mm, or fromabout 3 mm to about 20 mm). Point A (e.g., in FIG. 36) may reside on thetop surface of the first portion. Point B may reside on the bottomsurface of the second portion. The second portion may be a cavityceiling or hanging structure as part of the 3D object. Point B (e.g., inFIG. 36) may reside above point A. The gap may be the (e.g., shortest)distance (e.g., vertical distance) between points A and B. FIG. 36 showsan example of the gap 3640 that constitutes the shortest distance dABbetween points A and B. There may be a first normal to the bottomsurface of the second portion at point B. FIG. 36 shows an example of afirst normal 3612 to the surface 3620 at point B. The angle between thefirst normal 3612 and a direction of the gravitational accelerationvector 3600 (e.g., direction of the gravitational field) may be anyangle y. Point C may reside on the bottom surface of the second portion.There may be a second normal to the bottom surface of the second portionat point C. FIG. 36 shows an example of the second normal 3622 to thesurface 3620 at point C. The angle between the second normal 3622 andthe direction of the gravitational acceleration vector 3600 may be anyangle δ. Vectors 3611, and 3621 are parallel to the gravitationalacceleration vector 3600. The angles γ and δ may be the same ordifferent. The angle between the first normal 3612 and/or the secondnormal 3622 to the direction of the gravitational acceleration vector3600 may be any angle alpha. The angle between the first normal 3612and/or the second normal 3622 with respect to the normal to thesubstrate may be any angle alpha. The angles γ and δ may be any anglealpha. For example, alpha may be at most about 45°, 40°, 30°, 20°, 10°,5°, 3°, 2°, 1°, or 0.5°. The shortest distance between points B and Cmay be any value of the auxiliary support feature spacing distancementioned herein. For example, the shortest distance BC (e.g., d_(BC))may be at least about 0.1 millimeters (mm), 0.5 mm, 1 mm, 1.5 mm, 2 mm,3 mm, 4 mm, 5 mm, 10 mm, 15 mm, 20 mm, 25 mm, 30 mm 35 mm, 40 mm, 50 mm,100 mm, 200 mm, 300 mm, 400 mm, or 500 mm. As another example, theshortest distance BC may be at most about 500 mm, 400 mm, 300 mm, 200mm, 100 mm, 50 mm, 40 mm, 35 mm, 30 mm, 25 mm, 20 mm, 15 mm, 10 mm, 5mm, 4 mm, 3 mm, 2 mm, 1.5 mm, 1 mm, 0.5 mm, or 0.1 mm. FIG. 36 shows anexample of the shortest distance BC (e.g., 3630, d_(BC)). The bottomskin layer may be the first surface and/or the second surface. Thebottom skin layer may be the first formed layer of the 3D object. Thebottom skin layer may be the first formed hanging layer in the 3D object(e.g., that is separated by a gap from a previously formed layer of the3D object).

As understood herein: The solidus temperature of the material is atemperature wherein the material is in a solid state at a givenpressure. The liquefying temperature of the material is the temperatureat which at least part of the pre-transformed material transitions froma solid to a liquid phase at a given pressure. The liquefyingtemperature is equal to a liquidus temperature where the entire materialis in a liquid state at a given pressure.

In some embodiments, the 3D printer comprises one or more sensors. Thesensor may sense, detect, and/or observe a physical-attribute during the3D printing. The physical-attribute may correlate to and/or directlydetect (i) a temperature at one or more positions at the target surface,a power density of the (e.g., transforming) energy beam, (iii) a powerof an energy source that generates the energy beam, or (iv) anycombination thereof The physical attribute may comprise an irradiation(e.g., reflection) of a beam (e.g., electromagnetic beam) from thetarget surface. For example, the physical attribute may comprise awavelength, intensity, or duration, of the (e.g., electromagnetic) beam.The physical-attribute may be included in a spectroscopic measurement.The physical-attribute may be included in an (e.g., optical) image. Thephysical attribute may include a FLS of a melt pool formed at the targetsurface with the transforming energy beam (e.g., FIG. 26A, 2605), and/orits vicinity (e.g., 2610). The sensor measurement(s) may be used to: (i)provide quality assurance of the printed 3D object, (ii) providehistorical data that may be used to adjust a computer model relating tothe 3D printing, (iii) control in real-time one or more aspects of the3D printing, or (iv) any combination thereof

In some embodiments, the sensor measurement(s) and/or other 3D printingprocess parameter(s) may allow a user, client and/or customer todetermine if a 3D object passes a performance threshold (e.g., toprevent failure and/or mistakes in the 3D object's performance in itsintended purpose). The sensor measurement(s) and/or other 3D printingprocess parameter(s) may provide confidence that the qualityrequirements of the 3D object are fulfilled. The sensor measurement(s)and/or other 3D printing process parameter(s) may allow a user, clientand/or customer to ensure the quality of a 3D object. The qualityassurance may comprise (i) a comparison with a standard, (ii) monitoringof the 3D printing processes, or (iii) a feedback and/or closed loopcontrol. The standard may be based on historical data of previouslyprinted and/or otherwise manufactured respective 3D object. The standardmay relate to an industrial standard. The quality assurance may comprisea quality control of the 3D object. The quality assurance may comprise astatistical process control of the 3D printing. The quality assurancemay provide a fingerprint of the process for printing a resulting 3Dobject. The process fingerprint may allow a user, client, and/orcustomer to identify desired 3D object characteristics. The processfingerprint may allow a user, client and/or customer to sort the 3Dobject based on the process fingerprint. The process fingerprint maycorrelate to a 3D object build with the detected and/or recorded processparameters.

In some embodiments, the 3D printer comprises a computer model that isbased on a requested 3D object. The computer model may comprise 3Dprinting instructions of the requested 3D object. The computer model maycomprise a physical model that correspond to the behavior of thematerial (e.g., pre-transformed and/or transformed material) during the3D printing, which at least part of the material forms the 3D object.The physical model may be based on a simulation (e.g.,thermos-mechanical simulation). The physical model may comprise animitation of the physical manifestations that take place during the 3Dprinting. The physical model may comprise an approximation of thephysical manifestations that take place during the 3D printing. Theapproximation may be a rough approximation. The historical data may beused by the controller system (e.g., comprising the computer model) as alearning tool to form a learning control system. The historical data maybe used to vary one or more parameters of the computer model (e.g., ofthe physical model). The historical data may be used to adjust one ormore computer model (e.g., physical model) parameters in response to thesensor measurement(s) (e.g., as correlating to the respective processparameter(s)). The computer model (e.g., the physical model) may beadjusted, corrected, and/or fine-tuned using the historical dataprovides by the sensor measurement(s) (e.g., that relate to a of processparameter, or a set of process parameters).

In some embodiments, the 3D printer comprises a control system. Thecontrol system may be a real-time control system. The measurement(s)from the one or more sensors may be used to alter the printinginstructions for the 3D object in real time, during its printing. Themeasurement may comprise (i) a measurement of signals accumulated duringprinting of one or more layers of the 3D object, (ii) a measurement ofsignals accumulated during printing of one or more paths (e.g., hatches,or vectors) within a layer of the 3D object, (iii) a measurement ofsignals accumulated during printing of a plurality of melt pools forminga path (e.g., hatch, or vector) within a layer of the 3D object, or (iv)a measurement of signal(s) during printing of a single of melt pool. Theplurality of melt pools can ones (e.g., be less than ten melt pools),tens of melt pools, hudreds of melt pools, or thousands of melt pools.For example, the plurality of melt pools can be at least about 100, 200,300, 400, or 500 melt pools. The plurality of melt pools can be anynumber of melt pools between the afore mentioned numbers (e.g., fromones to thousands of melt pool, from tens to hundreds of melt pools, orfrom 100 to 500 melt pools). The real-time measurement(s) may be used to(i) alter a parameter value prescribed by the 3D printing instruction,(ii) alter the computer model (e.g., alter one or more parameters of thecomputer model) by using the measured signals, (iii) alter one or moreprinting parameter in real-time (e.g., using a feedback and/or closedloop control). Alter a parameter value prescribed by the 3D printinginstruction may comprise observing a systematic deviation from one ormore printing parameters (e.g., power of the energy source and/or powerdensity of the energy beam, that is required to reach a certaintemperature threshold). For example, the printing instructions (e.g.,comprising the computer model) may prescribed a first power value toreach a temperature threshold. During the 3D printing, a sensorindicates that the threshold temperature is reached with a second powervalue that is (e.g., systematically) lower by a percentage from thefirst prescribed power. The printing instructions may thus adjust theprescribed power to be lower. The adjustment may be after gainingconfidence that the overall adjustment is required. The adjustment maybe subsequent to (e.g., a real-time) observation of a systematicdeviation from the computer model prediction. The adjustment may be baya value (e.g., a percentage), or by a function. The function maycomprise a linear, polynomial, or logarithmic function. In someembodiments, the computer model parameters may be adjusted based on themeasurements. Confidence may relate to the noise level of the sensormeasurements. For example, temperature measurements of the targetsurface may be affected by heating spattered material that parts fromthe target surface, and obstructs the detector. The unreliablemeasurements may be confined to certain angle (or angle range) of theenergy beam with respect to the target surface. For example, to an angleof at least about 80° or 90° with the target surface; to an angle of atmost about 90° or 100° with the target surface or to an angle range fromabout 80° to about 100° of the energy beam with respect to the targetsurface (e.g., FIG. 5, 510).

In some embodiments, the formation of a melt pool is control inreal-time during the time of its formation. In some embodiments, thesensor (e.g., detector) may be coupled to at least one optical fiber(e.g., a fiber coupled to a detector). At times, the detector maycomprise a multiplicity of detectors. Each of the multiplicity ofdetectors may be coupled to a different optical fiber respectively. Attimes, an optical fiber may be coupled to a single detector. At times,at least two detectors may be coupled to an optical fiber. At times, atleast two optical fibers may be coupled to a detector. The differentoptical fibers may form an optical fiber bundle. The optical fiberdetector may comprise a magnifier and/or a de-magnifier coupled to afiber. The optical fiber bundle may be a coherent bundle of fiber. Theoptical fiber may split to two or more detectors. The optical fiberdetector may be positioned prior to the detector and after the opticalelement (e.g., filter, mirror, or beam splitter, whichever disposedbefore the optical fiber). At times, the detector may be a single (e.g.,pixel) detector. The detector may be devoid of (e.g., not include, orexclude) spatial information.

In some embodiments, different fiber groups within the fiber bundlesense different positions in the target surface. For example, thecentral fiber (e.g., FIG. 37, 3710) may sense the melt pool (e.g., FIG.26A, 2605), and the surrounding fibers (e.g., FIG. 37, 3720) may sensethe vicinity of the melt pool (e.g., FIG. 26A, 2610). FIG. 37 shows anexample of an optical fiber bundle (e.g., 3700). In some examples, thecentral fiber (e.g., 3710) may detect the (e.g., forming) melt pool(e.g., FIG. 26A, 2605), while closely surrounding fibers (e.g., 3720)detect positions in a ring around the melt pool (e.g., that is distancedd₁ away from the center); more distant surrounding fibers (e.g., 3730)detect positions at a ring that is distanced d₂ from the center etc. Atleast two (e.g., each of the) fibers within the fiber bundle may havedifferent cross sections (e.g., diameters thereof). At least two fiberswithin the fiber bundle may have (e.g., substantially) the same crosssection. For example, at least two fibers within a ring of fibers (e.g.,surrounding the central fiber) may have different cross sections (e.g.,diameters thereof). At least two fibers within a ring of fibers (e.g.,surrounding the central fiber) may have (e.g., substantially) the samecross section. In some embodiments, different fiber groups within thefiber bundle are directed to different detectors. For example, thecentral optical fiber (e.g., 3710) may be directed to a first detector.The first fiber ring (e.g., 3720) surrounding the central fiber may bedirected to a second detector. The second fiber ring (e.g., 3730)surrounding the central fiber may be directed to a third detector. Thethird fiber ring (e.g., 3740) surrounding the central fiber may bedirected to a fourth detector. The different detectors may form a groupof detectors. At least two (e.g., each of the) detectors within thegroup of detectors may detect signals pertaining to different areas ofthe target surface respectively. For example, At least two (e.g., eachof the) detectors within the group of detectors may detect signalspertaining to different distanced rings relative to the melt pool (e.g.,center thereof) respectively. The detectors may be connected to thecontrol system that may control one or more 3D printing parameters. Forexample, the one or more detectors may be used to control thetemperature at one or more positions in the material bed.

The optical fiber bundle may include one or more single (e.g., pixel)detectors. Each pixel detector may be optionally coupled to an opticalfiber. The optical fiber bundle may comprise a central fiber (e.g.,3710). One or more independent single detectors (e.g., at least 1, 2, 3,4, 5, 6, 7, 8, 9 or 10 detectors) coupled to one or more independentoptical fibers (e.g., at least 1, 2, 3, 4, 5, 6, 7, 8, 9 or 10 opticalfibers) respectively may be disposed adjacent to the central fiber. Forexample, the one or more independent optical fibers may engulf (e.g.,surround) the central fiber. The number of independent optical fibersthat engulf the central fiber may vary (e.g., the central fiber may beengulfed by at least 1, 2, 3, 4, 5, 6, 7, 8, 9 or 10 optical fibers).The engulfed optical fibers may be engulfed by one or more independentoptical fibers (e.g., the first one or more independent fibers adjacentto the central fiber may be engulfed by at least 1, 2, 3, 4, 5, 6, 7, 8,9 or 10 optical fibers). Engulf may be in at least one cross-sectionalcircular arrangement (e.g., FIG. 37). In some embodiments, the opticalfiber bundle comprises (i) another optical fiber that has a crosssection that is (e.g., substantially) the same as the cross section ofthe central optical fiber, or (ii) another optical fiber that has across section that is different (e.g., smaller, or larger) from thecross section of the central optical fiber. In some embodiments, the oneor more independent optical fibers have a cross section that is (e.g.,substantially) the same (e.g., 3720) as the cross section of the centraloptical fiber (e.g., 3710). In some embodiments, the one or moreindependent optical fibers have a cross section that is different thanthe cross section of the central optical fiber. For example, the one ormore independent optical fibers may have a cross section that is larger(e.g., 3730, 3740) than the cross section of the central optical fiber(e.g., 3710). The larger cross section of the optical fiber mayfacilitate detection of a returning energy beam striking a larger crosssection of the optical fiber, and thus allowing for detection of a lowerintensity energy beam. The adjacent one or more single detectors mayallow detection of energy beam that strikes an area larger than the areadetected by the central fiber. For example, the outermost singledetector (e.g., 3740) may detect (e.g., collect irradiation from) anarea that is larger than the area detected by the central fiber. Largermay comprise at least about 2, 3, 5, 10, 20, 25, 30, 35, 40, 45, 50, 55,60, 65, 70, 75, 80, 85, 90, 95 or 100 times larger area than the areadetected by the central fiber. Larger may comprise at most about 2, 3,5, 10, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95 or100 times larger area than the area detected by the central fiber. Theoutermost single detector may detect an area larger than the areadetected by the central fiber, wherein larger can be between any of theafore-mentioned values (e.g., 2 times to 100 times, from about 2 timesto about 30 times, from about 35 times to about 70 times, or from about75 times to about 100 times). The central fiber may detect a pixel atits highest resolution. As the detection area increases amongst thesurrounding single detectors, the surrounding fiber may detect one ormore lower resolution pixels. The at least one optical fiber in thebundle may be aligned with the portion of the energy beam that has thestrongest signal intensity (e.g., radiation energy). The one opticalfiber can be aligned (e.g., in real time) to be the central opticalfiber. As the detection area of the fiber detectors increase, the signalintensity may drop. The increasing area of the detector may allowimprovement of the signal (e.g., as the signal to noise ratiodecreases). The fiber bundle may allow maximizing the collection rate of(e.g., optical) information (e.g., by selecting a sample of opticalfiber detectors, by varying the sampling frequency of the detectors).The optical fiber bundle may be a lower cost alternative to thermalimaging detectors (e.g., In GaAs or Ge). The optical fiber bundle (e.g.,having varied cross sectional optical fibers), may allow quickerfocusing and/or signal detection.

In some embodiments, a first detector (e.g., operatively coupled tofiber FIG. 37, 3710) may sense at least one physical attribute of themelt pool (e.g., FIG. 26A, 2605), for example, during its formation. Forexample, the first detector may sense the radiation emitted and/orreflected from the melt pool. For example, the first detector may sensethe temperature, shape, and/or FLS of the melt pool. The FLS may be ofthe exposed surface of the melt pool. The shape may be circular, oval,or irregular. The first detector may be coupled to the energy beamfootprint on the target surface. In some embodiments, a second detector(e.g., FIG. 37, an equal radius ring of detectors operatively coupled tofibers comprising 3720) may sense at least one physical attribute of themelt pool vicinity (e.g., FIG. 26A, 2610), for example, during itsheating. The second detector may comprise a set of sensor. For example,the second detector may comprise a ring of detectors. The seconddetector may be ring shaped. The second detector may be concentric tothe first detector. The detected area of the second detector may beinclude or exclude the melt pool area. The signal that is detected bythe detector set of the second detector may be averaged to produce aphysical attribute value (e.g., amplitude value that correlates to atemperature value). The control system may compare the signal of thefirst detector to the second detector to receive a comparison value of aphysical attribute. The comparison value may facilitate estimation ofthe (i) isotropy of heat distribution within the melt pool, (ii)isotropy of melt pool shape (e.g., the horizontal and/or vertical crosssections of the melt pool), (iii) temperature gradients within the meltpool, or (iv) any combination thereof.

At times, the melt pool may be controlled to reach a first maximumphysical-attribute (e.g., temperature) threshold value. The firstdetector may facilitate (e.g., direct, in situ, and/or real time)controlling the physical-attribute (e.g., temperature) of the melt pool.For example, using the melt pool temperature, size, and/or shape, theenergy beam and/or source may be attenuated. Attenuated may comprisesaltering at least one characteristic of the energy beam and/or energysource. For example, reducing (e.g., stopping) the power of the energysource when the temperature of the melt pool reaches a first temperaturethreshold value. For example, reducing (e.g., stopping) the powerdensity of the energy beam when the temperature of the melt pool reachesthe first temperature threshold value. For example, reducing (e.g.,stopping) the cross section of the energy beam when the melt poolreaches the melt pool diameter threshold value.

At times, the melt pool may be controlled to reach a second maximumphysical-attributer (e.g., temperature) threshold value. The seconddetector (e.g., detector set) may facilitate (e.g., direct, in situ,and/or real time) controlling the physical-attribute (e.g., temperature)of the melt pool vicinity. For example, using the temperature, size,and/or shape, of the heated vicinity of the melt pool, the energy beamand/or source may be attenuated. Attenuated may comprises altering atleast one characteristic of the energy beam and/or energy source. Forexample, reducing (e.g., stopping) the power of the energy source whenthe temperature of the melt pool vicinity reaches a second temperaturethreshold value. For example, reducing (e.g., stopping) the powerdensity of the energy beam when the temperature of the melt poolvicinity reaches the second temperature threshold value. For example,reducing (e.g., stopping) the cross section of the energy beam when themelt pool vicinity reaches the melt pool vicinity diameter thresholdvalue.

In some embodiments, the first detector (detecting a physical attributeof the melt pool) and the second detector (detecting a physicalattribute of the melt pool vicinity) are used. The control system mayattenuate the energy beam and/or energy source to allow the melt pool toreach, maintain, and/or not exceed a first physical-attribute (e.g.,temperature) threshold value, while allowing the vicinity of the meltpool to reach, maintain, and/or not exceed a second physical attribute(e.g., temperature) threshold value. The control may be by altering oneor more characteristics of the energy beam and/or source. For example,the first detector (detecting a temperature of the melt pool) and thesecond detector (detecting a temperature of the melt pool vicinity) maybe used. The control system may attenuate the energy beam to allow themelt pool to reach, maintain, and/or not exceed a first temperaturethreshold value, while allowing the vicinity of the melt pool to reach,maintain, and/or not exceed a second temperature threshold value. Forexample, by altering (e.g., reducing) the power density of the energybeam, by altering the power of the energy source, by altering thediameter of the energy beam, by altering the focus of the energy beam,by altering the dwell time of the energy beam, or any combinationthereof. Altering may comprise, reducing or increasing. Reducing maycomprise ceasing. In some embodiments, the resulting melt pool ishomogenous in (i) temperature distribution gradient, (ii) shape, (iii)microstructure distribution, or (iv) any combination thereof The realtime melt pool control (e.g., using the two detectors) may allowformation of successive (e.g., substantially) homogenous and/orisotropic melt pools (e.g., FIG. 35). The (e.g., substantially)homogenous and/or isotropic melt pools may in a hatch line, path, layer,within the entire 3D object. At times, the usage of the two detectorsmay allow (e.g., controlled) formation of anisotropic melt pools, whoseanisotropy may be requested. For example, at times it may be requestedto form melt pools having aspect ratio that is different than 1:1 (inwhich the vertical cross sectional radius is equal to the horizontalcross sectional radius).

In some examples, the transforming energy beam irradiates (e.g.,injects) energy into one or more pre-formed layers (e.g., deeper layers)of hardened material that are disposed below the target layer (e.g.,layer of pre-transformed material) that is irradiated by thetransforming energy beam. The injection of energy into the one or moredeeper layers may heat those deeper layers up. Heating of the deeperlayers may allow those deeper layers to release stress (e.g.,elastically and/or plastically). For example, the heating of the deeperlayers may allow those layers to deform beyond the stress point. Forexample, the heating of the deeper layers may allow a position of thedeeper layer that is parallel to the irradiated position to reach anelevated temperature that is above the solidus temperature (e.g., and ator below the liquidus temperature), liquefy (e.g., become partiallyliquid), transform (e.g., melt), become liquidus (e.g., fully liquid),and/or plastically yield (e.g., stress-yield).

The control of the transforming energy beam may comprise substantiallyceasing (e.g., stopping) to irradiate the target area when thetemperature at the bottom skin reaches a target temperature. The targettemperature may comprise a temperature at which the material (e.g.,pre-transformed or hardened) reaches an elevated temperature that isabove the solidus temperature, transforms (e.g., re-transforms, e.g.,re-melts), become liquidus, and/or plastically yields. The control ofthe irradiating energy may comprise substantially reducing the energysupplied to (e.g., injected into) the target area when the temperatureat the bottom skin reached a target temperature. The control of theirradiated energy may comprise altering the energy profile of the energybeam and/or flux respectively. The control may be different (e.g., mayvary) for layers that are closer to the bottom skin layer as compared tolayers that are more distant from the bottom skin layer (e.g., beyondthe critical layer thickness as disclosed herein). The control maycomprise turning the irradiated energy on and off (e.g., at specifiedand/or controlled times). The control may comprise reducing the powerper unit area, cross section, focus, power, of the transforming energybeam. The control may comprise altering at least one property of thetransforming energy beam, which property may comprise the power, powerper unit area, cross section, energy profile, focus, scanning speed,pulse frequency (when applicable), or dwell time of the irradiatedenergy. During the intermission (e.g., “off”) times, the power and/orpower per unit area of the energy beam may be substantially reduced ascompared to its value at the dwell times (e.g., “on” times).Substantially may be in relation to the transformation of the materialat the target surface. During the intermission, the irradiated energymay relocate away from the area which was tiled, to a different area inthe material bed that is substantially distant from area which was tiled(see examples 1). During the dwell times, the irradiated energy mayrelocate back to the position adjacent to the area which was just tiled(e.g., as part of the transforming energy beam path). The control may bereal-time control (e.g., during the 3D printing process). The controlmay be dynamic control. The control may use at least one algorithm. Thecontrol may comprise closed loop control, or open loop control. Thecontrol may be closed loop control, open loop control or any combinationthereof.

FIG. 24 shows a schematic example of a (e.g., automatic) control system2400 that is programmed or otherwise configured to facilitate theformation of one or more 3D objects. The control system 2400 includes a(e.g., PID) controller 2440, a forming 3D object 2450, one or moresensors (e.g. temperature sensor) 2460, one or more computer models forthe physical process of 3D printing 2470 (e.g., comprising the physicalmodel or the control model). The control system may optionally include afeedback control loop such as 2430 or 2442. The feedback control loopmay comprise one or more logical switches (e.g., 2480). The logicalswitch may alter (e.g., turn “on” or “off”) a feedback loop control. Thealteration may utilize a calculated variable (e.g., temperature). Thecalculated variable may comprise a threshold value. The calculatedvariable may be compared to a respective measured variable. Thecalculated temperature may derive from the computer model (e.g., whichat least part of the computer model may be in 2470). For example, thecontrol scheme (e.g., FIG. 24) may comprise the control-model (e.g.,included in 2470). The control model may comprise one or morecalculations of the control variable (e.g., the temperature). Thecontrol model may comprise comparing a measured variable to itsrespective control variable (e.g., the calculated variable value,threshold variable value, and/or critical variable value).

The control system (e.g., 2400) may be configured to control (e.g. inreal time) a power of the energy source, speed of the energy beam, powerdensity of the energy beam, dwell time of the energy beam, energy beamfootprint (e.g., on the exposed surface of the material bed), and/orcross-section of the energy beam, to maintain a target parameter of oneor more forming 3D objects. The target parameter may comprise atemperature, or power of the energy beam and/or source. In someexamples, maintaining a target temperature for maintaining on one ormore characteristics of one or more melt pools. The characteristics ofthe melt pool may comprise its FLS, temperature, fluidity, viscosity,shape (e.g., of a melt pool cross section), volume, or overall shape.The control system (e.g., 2400) may be configured to control (e.g. inreal time) a temperature, to maintain a target parameter of one or moreforming 3D objects, e.g., a target temperature of one or more positionsof the material bed to maintain on one or more melt pools. The one ormore positions may comprise a position within a melt pool, adjacent tothe melt pool, or far from the melt pool. Adjacent to the melt pool maybe within a distance (e.g., radius) of at least about 1, 2, 3, 4, or 5average melt pool diameters. Adjacent to the melt pool may be within adistance of at most about 1, 2, 3, 4, or 5 average melt pool diameters.Adjacent to may be any distance between the afore mentioned distances(e.g., from about 1 to about 5 average melt pool diameters). FIG. 26Ashows an example of a melt pool 2605 shown as a top view, having adiameter d_(i). The melt pool 2605 in the example shown in FIG. 26A, issurrounded by an area that is centered at the melt pool, and extends(for example) two melt pool diameters after the edge of the melt pool2605, designated as d₂ and d₃, wherein d₁, d₂ and d₃ are (e.g.,substantially) equal. FIG. 26B shows an example of a vertical crosssection in a material bed 2625 in which a melt pool 2615 is disposed,which to view of the melt pool 2615 has a diameter d₁. The material bed2625 has an exposed surface 2629. The area surrounding the melt pool2620 extends beyond the melt pool (e.g., into the material bed). Thearea 2620 extends away from the melt pool by (for example) two melt pooltop view diameters d₂ and d₃, as measured from the edge of the melt pool2615, wherein d₁, d₂ and d₃ are (e.g., substantially) equal. The controlsystem may use one or more signals detected from one or more positionsat the melt pool and/or from a position adjacent to the melt pool (e.g.,FIG. 26A). The signals may be used to determine a temperature at the oneor more positions. The one or more signals may be used in forming thephysical-model (e.g., operatively coupled to the control-model). Thematerial bed may be a box, a cylinder, or a prism (e.g., a right prism).The cylinder may be an elliptical cylinder (e.g., circular cylinder).The cylinder may be a right cylinder. The prism may have a polygonalcross section. For example, the prism may be a triangular, rectangular,pentagonal, hexagonal, or a heptagonal prism. The FLS (e.g., width,depth, and/or height) of the material bed can be at least about 50millimeters (mm), 60 mm, 70 mm, 80 mm, 90 mm, 100 mm, 200 mm, 250 mm,280 mm, 400 mm, 500 mm, 800 mm, 900 mm, 1 meter (m), 2 m or 5 m. The FLS(e.g., width, depth, and/or height) of the material bed can be at mostabout 50 millimeters (mm), 60 mm, 70 mm, 80 mm, 90 mm, 100 mm, 200 mm,250 mm, 280 mm, 400 mm, 500 mm, 800 mm, 900 mm, 1 meter (m), 2 m or 5 m.The FLS of the material bed can be between any of the aforementionedvalues (e.g., from about 50 mm to about 5 m, from about 250 mm to about500 mm, from about 280 mm to about 1 m, or from about 500 mm to about 5m).

The one or more forming 3D objects can be formed (e.g., substantially)simultaneously, or sequentially. The one or more 3D objects can beformed in a (e.g., single) material bed. The controller may receive atarget parameter (e.g., 2405) (e.g., temperature) to maintain at leastone characteristic of the forming 3D object. Examples of characteristicsof forming 3D objects include temperature and/or metrologicalattribute(s) (e.g., information) of a melt pool. The metrologicalattribute(s) (e.g., information) of the melt pool may comprise its FLS.Examples of characteristics of forming 3D objects include metrologicalattribute(s) (e.g., information) of the forming 3D object. For example,geometry attribute(s) (e.g., information. E.g. height) of the forming 3Dobject. Examples of characteristics of forming 3D objects includematerial characteristic such as hard, soft and/or fluid (e.g., liquidus)state of the forming 3D object. The target parameter may be time varyingor location varying or a series of values per location or time. Thetarget parameter may vary in time and/or location. The controller may(e.g., further) receive a pre-determined control variable (e.g. powerper unit area of the energy beam) target value from a control loop suchas, for example, a feed forward control (e.g., 2410). In some examples,the control variable controls the value of the target parameter of theforming 3D object. For example, a predetermined (e.g., threshold) valueof power per unit area of the energy beam may control the temperature(e.g., range) of the melt pool forming the 3D object.

A computer model (e.g., comprising a prediction model, statisticalmodel, a thermal model, or a thermo-mechanical model) may predict and/orestimate one or more physical parameters of the forming 3D object. Thecomputer model may comprise a geometric model (e.g., comprising OPC), ora physical model. The computer model may provide feedforward informationto the controller. The computer model may provide the open loop control.There may be more than one computer models (e.g. at least 1, 2, 3, 4, 5,6, 7, 8, 9 or 10 different computer models). The controller may (e.g.,dynamically) switch between the computer models to predict and/orestimate the one or more physical parameters of the forming 3D object.Dynamic includes changing computer models (e.g., in real time) based ona user input, or based on a controller decision that may in turn bebased on monitored target variables of the forming 3D object. Thedynamic switch may be performed in real-time (e.g., during the formingof the 3D object). Real time may be, for example, during the formationof a layer of transformed material, during the formation of a layer ofhardened material, during formation of a portion of a 3D object, duringformation of a melt pool, during formation of an entire 3D object, orany combination thereof The controller may be configured (e.g.,reconfigured) to include additional one or more computer models and/orreadjust the existing one or more computer models. A prediction of theone or more parameters of the forming 3D object may be done offline(e.g. predetermined) and/or in real-time. The at least one computermodel may receive sensed parameter(s) value(s) from one or more sensors.The sensed parameter(s) value(s) may comprise temperature sensed withinand/or in the vicinity of one or more melt pools. Vicinity may be withina radius of at least about 1, 2, 3, 4, or 5 average melt pool FLS from aforming melt pool. The computer model may use (e.g., in real-time) thesensed parameter(s) value(s) for a prediction and/or adjustment of thetarget parameter. The computer model may use (e.g., in real-time)geometric information associated with the requested and/or forming 3Dobject (e.g. melt pool geometry). The use may be in real-time, and/oroff-line. Real time may comprise during the operation of the energy beamand/or source. Off-line may be during the time a 3D object is notprinted and/or during “off” time of the energy beam and/or source. Thecomputer model may compare a sensed value (e.g., by the one or moresensors) to an estimated value of the target parameter. The computermodel may (e.g., further) calculate an error term (e.g., 2426) andreadjust the at least one computer model to achieve convergence (e.g.,of a desired or requested 3D model with the printed 3D object).

The computer model may estimate a target variable (e.g., 2472). Thetarget variable may be of a physical-attribute that may or may not be(e.g., directly) detectable. For example, the target variable may be ofa temperature that may or may not be (e.g., directly) measurable. Forexample, the target variable may be of a physical location that may ormay not be (e.g., directly) measurable. For example, a physical locationmay be inside the 3D object at a depth that may be not be directlymeasured by the one or more sensors. An estimated value of the targetvariable may be (e.g., further) compared to a critical value of thetarget variable. At times, the target value exceeds the critical value,and the computer model may provide feedback to the controller toattenuate (e.g., turn off, or reduce the intensity of) the energy beam(e.g., for a specific amount of time). The computer model may set up afeedback control loop (e.g., 2430), for example, by providingfeedforward information. The feedback control loop may be for thepurpose of adjusting one or more target parameters to achieveconvergence (e.g., of a desired or requested 3D model with the printed3D object). In some embodiments, the computer model may predict (i) anestimated temperature of the melt pool, (ii) local deformation withinthe forming 3D object, (iii) global deformation and/or (iv) temperaturefields. The computer model may (e.g. further) predict corrective energybeam adjustments (e.g. in relation to a temperature target threshold).The adjustment predictions may be based on the (i) measured and/ormonitored temperature information at a first location on the forming 3Dobject (e.g. a forming melt pool) and/or (ii) at a second location (e.g.in the vicinity of the forming melt pool) and/or (iii) geometricinformation (e.g. height) of the forming 3D object. The energy beamadjustment may comprise adjusting at least one control variablepertaining to a characteristics of the energy beam (e.g. power per unitarea, dwell time, cross-sectional diameter, and/or speed). In someembodiments, the control system may comprise a closed loop (e.g., andfeed forward) control, that may override one or more (e.g., any)corrections and/or predictions by the computer model. The override maybe effectuated by forcing a predefined amount of energy (e.g. power perunit area) to supply to the portion (e.g., of the material bed and/or ofthe 3D object). Real time may be during formation of at least one: 3Dobject, layer within the 3D object, dwell time of an energy beam along apath, dwell time of an energy beam along a hatch line, dwell time of anenergy beam forming a melt pool, or any combination thereof The controlmay comprise controlling a cooling rate (e.g., of the material bed, the3D object, or a portion thereof), control the microstructure of atransformed material portion, or control the microstructure of at leasta portion of the 3D object. Controlling the microstructure may comprisecontrolling the phase, morphology, FLS, volume, or overall shape of thetransformed (e.g., and subsequently solidified) material portion. Thematerial portion may be a melt pool.

In some embodiments, the control system comprises a first temperaturesensor and a second temperature sensor. The first temperature sensor mayprovide sensed information to the control system (e.g., to the PIDcontroller). The second temperature sensor may be compared to a criticaltemperature threshold in the control model. The control model may changebased on the input from the second and/or first temperature sensor. Thefirst temperature sensor may sense a temperature designated for the meltpool (e.g., FIG. 26A, 2605). The second temperature sensor may sense atemperature designated for the melt pool vicinity (e.g., FIG. 26A,2610). In some embodiments, when a temperature sensed by the firstand/or second sensor reaches and/or exceeds a certain (e.g., respective)threshold value, the irradiation of that area by the transforming energybeam may alter (e.g., reduce, e.g., cease). Altered irradiation maycomprise irradiation with an altered power density, cross section, dwelltime, and/or focus. The temperature sensed by the two sensors may beused to evaluate (e.g., calculate) the temperature gradient in thevicinity of the area designated for the melt pool (e.g., temperaturegradient between 2605 and 2610). The control model may be operativelycoupled (e.g., inform) the controller (e.g., comprising close loop orfeedback control loop). (E.g., 2442, 2426 and/or 2430).

The 3D object may be generated by providing a first layer ofpre-transformed material (e.g., powder) in an enclosure; transforming atleast a portion of the pre-transformed material in the first layer toform a transformed material. The 3D object may be generated by providinga pre-transformed material (e.g., stream) to a target surface (e.g.,platform); transforming at least a portion of the pre-transformedmaterial (i) prior to reaching the target surface or (ii) at the targetsurface, to form a transformed material. The stream can be a stream of aparticulate material. The transforming may be effectuated (e.g.conducted) with the aid of an energy beam. The energy beam may travelalong a path. The path may comprise hatching. The path may comprise avector or a raster path. The method for generating the 3D object mayfurther comprise hardening the transformed material to form a hardenedmaterial as part of the 3D object. In some embodiments, the transformedmaterial may be the hardened material as part of the 3D object. Themethod may further comprise providing a second layer of pre-transformedmaterial adjacent to (e.g., above) the first layer and repeating thetransformation process delineated herein (e.g., above). The method mayfurther comprise providing pre-transformed material adjacent to (e.g.,above) the first layer of hardened material (as part of the 3D object)and repeating the transformation process delineated herein.

The 3D object can be an extensive and/or complex 3D object. The 3Dobject can be a large 3D object. The 3D object may comprise a largehanging structure (e.g., wire, ledge, or shelf). Large may be a 3Dobject having a fundamental length scale of at least about 1 centimeter(cm), 1.5 cm, 2 cm, 10 cm, 20 cm, 30 cm, 40 cm, 50 cm, 60 cm, 70 cm, 80cm, 90 cm, 1 m, 2 m, 3 m, 4 m, 5 m, 10 m, 50 m, 80 m, or 100 m. In someinstances, The fundamental length scale (e.g., the diameter, sphericalequivalent diameter, diameter of a bounding circle, or largest ofheight, width and length; abbreviated herein as “FLS”) of the printed 3Dobject can be at least about 25 micrometers (μm), 50 μm, 80 μm, 100 μm,120 μm, 150 μm, 170 μm, 200 μm, 230 μm, 250 μm, 270 μm, 300 μm, 400 μm,500 μm, 600 μm, 700 μm, 800 μm, 1 millimeter (mm), 1.5 mm, 2 mm, 5 mm, 1centimeter (cm), 1.5 cm, 2 cm, 10 cm, 20 cm, 30 cm, 40 cm, 50 cm, 60 cm,70 cm, 80 cm, 90 cm, 1 m, 2 m, 3 m, 4 m, 5 m, 10 m, 50 m, 80 m, or 100m. The FLS of the printed 3D object can be at most about 1000 m, 500 m,100 m, 80 m, 50 m, 10 m, 5 m, 4 m, 3 m, 2 m, 1 m, 90 cm, 80 cm, 60 cm,50 cm, 40 cm, 30 cm, 20 cm, 10 cm, or 5 cm. In some cases, the FLS ofthe printed 3D object may be in between any of the afore-mentioned FLSs(e.g., from about 50 μm to about 1000 m, from about 120 μm to about 1000m, from about 120 μm to about 10 m, from about 200 μm to about 1 m, fromabout 1 cm to about 100 m, from about 1 cm to about 1 m, from about 1 mto about 100 m, or from about 150 μm to about 10 m). The FLS (e.g.,horizontal FLS) of the layer of hardened material may have any valuelisted herein for the FLS of the 3D object (e.g., from about 25 μm toabout 2000 μm). The example in FIG. 10C shows a horizontal portion 1001of the layer of hardened material (e.g., the top layer in the 10Cscheme). The example in FIG. 8 shows a top view of the layer of hardenedmaterial, which is a horizontal portion of the layer of hardenedmaterial. The example in FIG. 5 shows a vertical portion “h|” of thelayer of hardened material 546, indicating its height.

The methods, systems, software and/or apparatuses may include measuring,controlling and/or monitoring the deformation (e.g., curvature) of theforming and/or formed layer of hardened material (e.g., as it forms).The methods, systems, software and/or apparatuses may include measuring,controlling and/or monitoring the deformation of the forming and/orformed layer of hardened material or portion thereof (e.g., duringformation of the 3D object). During the formation of the 3D object maycomprise during formation of the layer or a portion thereof. During theformation of the 3D object may in some instances include subsequent tothe formation of the entire 3D object (e.g., a hardening period). Duringthe formation of the 3D object may in some instances exclude subsequentto the formation of the entire 3D object (e.g., exclude a period atwhich the 3D object has been formed, and it is left for completehardening).

At times, some portions of the 3D object may deform during its formation(e.g., during the transformation and/or hardening). The deformation maycomprise an undesired or a desired deformation. In some instances, thedeformation is undesired. The deformation may cause the 3D object to(e.g., substantially) deviate from the desired (e.g., requested) 3Dobject. For example, at least some portions of the 3D object may deform.Deform may comprise warp, buckle, bend, twist, shrink, or expand (e.g.,during formation or subsequent thereto) in a substantial and/orundesirable manner. Substantial may be relative to the intended purposeof the 3D object. For example, some portions of the 3D object may formwarped, buckled, bent, twisted, shrunk, or expanded portions that aresubstantial and/or not desirable. In some instances, it is desirable tocontrol (e.g., regulate and/or manipulate) the manner in which at leasta portion of the 3D object is formed (e.g., regarding any deformationand/or deviation from the desired 3D object). Control may compriseregulate, manipulate, restrict, direct, monitor, adjust, or manage. Insome instances, it is desirable to control the manner in which at leasta portion of the 3D object is formed (e.g., hardened). In someinstances, it is desired to control at least one characteristic of theat least a portion of the 3D object as it is formed (e.g., andhardened). The portion may be at least a portion of a layer of the 3Dobject. The portion may be a portion of the layer of the 3D object orthe entire layer thereof The at least one characteristic of the at leastportion of the 3D object may comprise a curvature. The curvature may beof the at least one layer (or portion thereof) that forms the 3D object.The curvature may be a positive or negative curvature. The curvature mayhave a radius of curvature.

The radius of curvature, “r,” of a curve at a point can be a measure ofthe radius of the circular arc (e.g., FIG. 7, 716) which bestapproximates the curve at that point. The radius of curvature can be theinverse of the curvature. In the case of a 3D curve (also herein a“space curve”), the radius of curvature may be the length of thecurvature vector. The curvature vector can comprise of a curvature(e.g., the inverse of the radius of curvature) having a particulardirection. For example, the particular direction can be the directiontowards the platform (e.g., designated herein as negative curvature), oraway from the platform (e.g., designated herein as positive curvature).For example, the particular direction can be the direction towards thedirection of the gravitational field (e.g., designated herein asnegative curvature), or opposite to the direction of the gravitationalfield (e.g., designated herein as positive curvature). A curve (alsoherein a “curved line”) can be an object similar to a line that is notrequired to be straight. A straight line can be a special case of curvedline wherein the curvature is (e.g., substantially) zero. A line of(e.g., substantially) zero curvature has an (e.g., substantially)infinite radius of curvature. A curve can be in two-dimensions (e.g.,vertical cross section of a plane), or in three-dimension (e.g.,curvature of a plane). The curve may represent a cross section of acurved plane. A straight line may represent a cross section of a flat(e.g., planar) plane. The platform may be a building platform. Theplatform may comprise the substrate, base, or bottom of the enclosure.The material bed may be operatively coupled and/or disposed adjacent to(e.g., on) the platform.

The methods, systems, software, and/or apparatus may compriseanticipating (e.g., calculating) the deformation. Anticipation may takeinto account a position and/or temperature measurements from at leastone sensor. The sensor may measure at least one position of a targetsurface (e.g., an exposed surface of the material bed) (e.g., asdescribed herein).

In some embodiments, the energy beam irradiates (e.g., flash, flare,shine, or stream) energy on a position of the exposed surface of thematerial bed for a period of time (e.g., predetermined period of time)to transform at least a portion of the pre-transformed material in thematerial bed into a transformed material. The remainder of the materialbed that has not been irradiated, may be at an average (or mean) ambienttemperature. The remainder of the material bed that has not beenirradiated, may be cooled (e.g., using a cooling member). The remainderof the material bed that has not been irradiated, may be not be activelyheated (e.g., using a radiative heater). The energy beam that transformsa pre-transformed material into a transformed material is designated as“transforming energy beam.” The transforming energy beam may travelalong a path (e.g., vector or raster path). The transformed material maybe a welded material. The transformed material may be a fused material.Fused may comprise molten (e.g., completely molten) or sintered. Thetime during which the transforming energy beam irradiates the materialbed may be referred to as a dwell time of the (transforming) energybeam. The irradiation of the material bed by the transforming energybeam may form a transformed portion of the pre-transformed materialwithin the material bed. For example, the irradiation of the powder bedby the transforming energy beam (e.g., laser) may form a fused portionof the powder material within the powder bed. During this period of time(i.e., dwell time) the energy flux of the transforming energy beam maybe substantially homogenous. Without wishing to be bound to theory,Energy flux may refer to the transfer rate of energy per unit area(e.g., having SI units: W·m⁻²=J·m⁻²·s⁻¹). Homogenous may refer to theflux of energy during the dwell time. Homogenous may refer to thedistribution of energy density across the cross section of the energybeam. In some instances, the distribution of energy density across thecross section of the energy beam may substantially resemble a Gaussiandistribution.

In some embodiments, at a certain period of time, the distribution ofenergy across the cross section of the energy beam may substantiallydiffer from a Gaussian distribution. During this period of time, thetransforming energy beam may (e.g., substantially) not translate (e.g.,neither in a raster form nor in a vector form). During this period oftime the energy density across the cross section of the transformingenergy beam may be (e.g., substantially) constant. In some embodiments,(e.g., during this period of time) the energy density of thetransforming energy beam may vary. n some embodiments, (e.g., duringthis period of time) the power of the energy source generating oftransforming energy beam, may vary. The variation may be predetermined.The variation may be controlled (e.g., by a controller). The controllermay determine the variation based on a signal received by one or moresensors (e.g., temperature and/or positional sensors). The controllermay determine the variation based on an algorithm.

In some embodiments, at least one controller is employed to effectuate(e.g., using control) a desired behavior of an apparatus and/or system(e.g., using at least one sensor). The control may comprise closed loopcontrol. The control may comprise feedback control. The control maycomprise feed forward control. The closed loop control may be based ondata obtained from one or more sensors. The closed loop control maycomprise closed loop control while processing one or more layersdisposed within the material bed (e.g., build planes). The closed loopcontrol may comprise closed loop control while processing at least aportion of the one or more build planes (e.g., the entire build). Thecontrolled variation may be based on closed loop and/or open loopcontrol. For example, the controlled variation may be based on (e.g.,utilizes) closed loop control. The closed loop control may be performedduring the 3D printing process. The closed loop control may rely on insitu measurements (e.g., of an exposed surface). The in situmeasurements may be in the chamber where the 3D object is generated(e.g., processing chamber). The closed loop control may rely on realtime measurements (e.g., during the 3D printing process of the at leastone 3D object). The closed loop control may rely on real timemeasurements (e.g., during formation of a layer of the 3D object). Thevariation may be determined based on one or more signals obtained from atemperature sensor and/or positional sensor (e.g., imaging). Thepositional sensor may be a metrology sensor (e.g., as described herein).The variation may be determined based on height variation measurements.The variation may be determined by height evaluation of the exposedsurface of the material bed, portions thereof, or any protruding objecttherefrom. The variation may be determined by temperature measurementsof the exposed surface of the material bed, portions thereof, or anyprotruding object therefrom. The variation may be determined bytemperature measurements of the transformed material (e.g., a melt pooltherein). The variation may be determined by melt pool size (e.g., FLS)evaluation of the transformed material.

In some embodiments, the control system evolves during at least aportion of the 3D printing (e.g., in real time, e.g., as delineatedherein). The evolution may utilize one or more parameters which vary inreal-time (e.g., during formation of a melt pool, or two successive meltpools). The evolution may use uncertain parameter values (e.g., whichuncertain parameter values may be roughly estimated). The (e.g.,real-time) evolution may rely on at least one changing condition duringat least a portion of the 3D printing. The changing conditions maycomprise a temperature of a portion at the target surface (e.g., targetsurface area of a footprint of the energy beam, and/or its vicinity), atleast one characteristic of the energy beam, and/or power of the energysource. The changing condition may comprise amount of plasma, oxygen,and/or moisture above the target surface (e.g., in the atmosphere of theprocessing chamber). The control system may comprise adaptive control.The adaptive control may comprise feed forward adaptive control, orfeedback adaptive control. The adaptive control may comprise a directadaptive control method (e.g., the estimated parameters are directlyused in the adaptive controller), or an indirect adaptive control method(e.g., the estimated parameters are used to calculate the controllerparameters). The adaptive control may comprise parameter estimation. Forexample, the computer-model may comprise an initial parameterestimation. For example, the physical-model and/or control-model maycomprise an initial parameter estimation. The estimated parameter may begeometric, temperature (e.g., emitted from the target surface), power ofthe energy source, and/or power density of the energy beam. The adaptivecontrol may comprise recursive parameter estimation. The adaptivecontrol may comprise reference adaptive control scheme (MRAC). The MRACmay comprise one-step-ahead adaptive control (OSAAC) scheme. In someembodiments, the control system may comprise a control algorithm thatevolves (e.g., changes) during the (e.g., real-time) control. Theadaptive control may comprise a parametric control scheme.

In some embodiments, the control system comprises a model predictivecontrol. The model predictive control may comprise the adaptive control.The control system may alter the physical model in real time. Thephysical model may comprise an electronic circuit. The physical modelmay comprise changing the electronic circuit in real time. For example,(i) changing the electronic connectivity in the electronic circuit inreal time, and/or (ii) changing the components (e.g., in type, number,and/or configuration) of the electronic circuit in real time. Thecontrol system may comprise changing the physical model (e.g., inreal-time) based on the timing of measured one or more events in the 3Dprinting (e.g., as sensed and/or detected, e.g., in real-time). Thecomputer model (e.g., physical model) may be a coarse prediction of oneor more aspects of the 3D printing. The measured (e.g., sensed and/ordetected) one or more parameters may allow fine tuning of that coarseprediction (e.g., in real time) to more accurately predict the 3Dprinting. The model predictive control may comprise an arbitrary model(e.g., any physical model, e.g., the electronic circuitry model). Thearbitrary model may comprise imitation of the 3D printing process. Thearbitrary model may comprise simulation of the 3D printing process. Theimitation and/or prediction may be a coarse (e.g., simplistic)prediction. Measured one or more parameters may allow fine tuning of thearbitrary model to better imitate and/or predict the 3D printing. Thephysical model may change dynamically in real time (e.g. during printingof a layer of the 3D object).

In some embodiments, the control system comprises robust control. Thecontrol system may comprise bounds to one or more variables. In someembodiments, the control system comprises an algorithm that isunchanging during the (e.g., real-time) control. The robust control maycomprise a non-parametric control scheme.

In some embodiments, the control comprises a closed loop control, or anopen loop control (e.g., based on energy calculations comprising analgorithm). The closed loop control may comprise feed back or feedforward control. The control may comprise generating a slicing plan of adesired model of the 3D object. The control may comprise generating apath plan (e.g., comprising a hatching plan) of a particular 3D modelslice, along which path the energy beam (e.g., transforming energy beam)may travel. Various path plans are delineated in Provisional PatentApplication Ser. No. 62/317,070, filed on Apr. 1, 2016, titled“APPARATUSES, SYSTEMS AND METHODS FOR EFFICIENT THREE-DIMENSIONALPRINTING” and PCT application number PCT/US16/66000 filed on Dec. 9,2016 titled “SKILLFUL THREE-DIMENSIONAL PRINTING”, both of which areincorporated by reference in their entirety. The path plan may be usedto generate at least one 3D printing direction according to which the 3Dprinting is conducted and/or controlled. The control may comprise usingan algorithm (e.g., comprised in a script). The algorithm may beembedded in a script. In some examples, a script is a language specificcomputer readable media (e.g., software) implementation of thealgorithm. For example, the model may combine feedback or feed-forwardcontrol based on an algorithm. The algorithm may take into account oneor more temperature measurements (e.g., as delineated herein), one ormore power measurements, one or more power density measurements,geometry of at least part of the 3D object, heat depletion/conductanceprofile of at least part of the 3D object, or any combination thereofThe controller may modulate the energy beam (e.g., transforming energybeam). The algorithm may take into account geometric pre-correction ofan object (i.e., object pre-print correction, OPC) to compensate for anydistortion of the final 3D object (e.g., after its hardening). FIG. 6shows various examples of OPC. The algorithm may comprise an instructionto form a correctively deformed object. The algorithm may comprisemodification applied to the model of a desired 3D object. Examples ofmodifications (e.g., corrective deformations) can be found in patentapplication No. 62/239805, titled “SYSTEMS, APPARATUSES AND METHODS FORTHREE-DIMENSIONAL PRINTING, AS WELL AS THREE-DIMENSIONAL OBJECTS” thatwas filed on Oct. 9, 2015, and PCT application number PCT/US16/34857titled “THREE-DIMENSIONAL PRINTING AND THREE-DIMENSIONAL OBJECTS FORMEDUSING THE SAME” that was filed on May 27, 2016, both of which areincorporated herein by reference in their entirety. The algorithm mayconsider the geometry of one or two different portion of the 3D object.The algorithm may be different for at least two (e.g., geometricallydifferent) portion of the 3D object. The different portions of the 3Dobject may comprise a bulk (e.g., interior) of the 3D object, bottomskin layer, surface of the 3D object, interior of the 3D objectimmediately close to the surface. The algorithm may be differ dependingon the angle of the bottom skin layer, with respect to the platform. Thebulk of the 3D object may comprise transformed (e.g., and hardened)material that is thick enough to withstand stress deformation uponadding transformed material to it (e.g., additional layer of transformedmaterial). For example, the control may comprise a thermoplasticsimulation. The thermo-mechanical simulation can comprise elastic orplastic simulation. The thermoplastic simulation may comprisemetrological and/or temperature measurements taken during the 3Dprinting process (e.g., of a previously formed layer of hardenedmaterial). The thermoplastic simulation may be used to revise the 3Dprinting plan, path plan, and/or path directionality. The analysis(e.g., thermoplastic simulation) may be performed before, during, and/orafter a layer of hardened material is formed. The transforming energybeam can be any energy beam delineated in Provisional Patent Applicationserial number 62/317,070 that is entirely incorporated by referenceherein.

In some embodiments, the printing instructions for two geometricallydifferent portions of the 3D object may be different. Different may beby at least one printing parameters. For example, different may be by atleast one characteristic of the transforming energy beam and/or energysource. The printing instructions be different for at least two (e.g.,geometrically different) portion of the 3D object. The differentportions of the 3D object may comprise a bulk (e.g., interior) of the 3Dobject, bottom skin layer, surface of the 3D object, interior of the 3Dobject immediately close to the surface. The printing instruction may bediffer depending on the angle of the bottom skin layer, with respect tothe platform.

At times, one or more 3D model slices are adjusted by the operationcomprising an algorithm to form an adjusted 3D model slice (e.g., analgorithm comprising OPC). A slice is a virtual portion of the requestedmodel of the 3D object that is materialized as a layer in the printed(e.g., physical) 3D object. The slice may be a cross section of themodel of the requested 3D object. The adjusted 3D model slice may be fedinto the controller to control the printing of the 3D object. Forexample, the adjusted 3D model slice may be fed into the controller tocontrol at least one apparatus within the 3D printing system (e.g., theenergy source and/or beam).

In some embodiments, the control (e.g., open loop control) comprises acalculation. The control may comprise using an algorithm. The controlmay comprise feedback loop control. In some examples, the control maycomprise open loop (e.g., empirical calculations), closed loop (e.g.,feed forward and/or feed back loop) control, or any combination thereofThe control setpoint may comprise a calculated (e.g., predicted)setpoint value. The setpoint may comprise adjustment according to theclosed loop control. The controller may use metrological and/ortemperature measurements. The controller may use material measurements.For example, the controller may use porosity and/or roughnessmeasurements (e.g., of the layer of hardened material). The controllermay direct adjustment of one or more systems, software module, and/orapparatuses in the 3D printing system. For example, the controller maydirect adjustment of the force exerted by the material removal mechanism(e.g., force of vacuum suction).

At times, a portion of the material within the material bed (e.g. FIG.1, 104) or a portion of the exposed material of the material bed (e.g.FIG.1, 106) may part from the material bed (e.g., due to heating). Theenergy beam may irradiate the material bed and cause the at least aportion to heat (e.g., overheat). Parting of the at least a portion mayform a suspended material in the atmosphere above the exposed surface.(e.g., in the enclosure 116). Parting from the material bed may causethe at least a portion to become airborne. Heating may cause the atleast a portion to undergo phase transformation. The phasetransformation may comprise transformation into a gas or into plasma.The phase transformation may occur during the formation of the one ormore 3D objects (e.g., during the transformation and/or hardening). Theparting from the material bed (e.g., evaporation) may lead to generationof debris (e.g., upon reaction and/or condensation). For example, the 3Dprinting process may comprise transforming a pre-transformed material toa transformed material by exposing it to a transforming energy beam fora (e.g. predefined) time period. The time at which the energy sourceemits a transforming energy beam may be referred herein as “dwell time”.The dwell time may be at least about 1 μsec, 2 μsec, 3 μsec, 4 μsec, 5μsec, 10 μsec, 20 μsec, 30 μsec, 40 μsec, 50 μsec, 60 μsec, 70 μsecs, 80μsec, 90 μsec, 100 μsec, 200 μsec, 500 μsec, 1 millisecond (msec), 3msec, 5 msec, or 10 msec. The dwell time may be any value between theaforementioned values (e.g., from about 1 μsec to about 60 μsec, fromabout 1 μsec to about 500 μsec, from about 1 μsec to about 10 msec, fromabout 500 μsec to about 5 msec, or from about 60 μsec to about 1001μsec). The power per unit area of the energy beam may be at least about100 Watt per millimeter square (W/mm²), 200 W/mm², 300 W/mm², 400 W/mm²,500 W/mm², 600 W/mm², 700 W/mm², 800 W/mm², 900 W/mm², 1000 W/mm², 2000W/mm², 3000 W/mm², 5000 W/mm2, 7000 W/mm², or 10000 W/mm². The power perunit area of the energy beam may be any value between theafore-mentioned values (e.g., from about 100 W/mm² to about 3000 W/mm²,from about 100 W/mm² to about 5000 W/mm², from about 100 W/mm² to about10000 W/mm², from about 100 W/mm² to about 500 W/mm², from about 1000W/mm² to about 3000 W/mm², from about 1000 W/mm² to about 3000 W/mm², orfrom about 500 W/mm² to about 1000 W/mm²). The power per unit area ofthe energy beam may be any power per unit are disclosed herein. Thedwell time or the amount of heat deposited by the energy beam may beused to transform the pre-transformed material to a transformedmaterial. The transformation may occur at a temperature that may causeone or more phase transformation of the at least a portion of thematerial bed (e.g., forming liquid, evaporation, and/or plasmaformation). In some instances, the at least a portion that is heated(e.g., by the energy beam) may comprise a pre-transformed material or atransformed material. At times, the at least a portion that is heated(e.g., by the energy beam) may comprise a hardened material.

Some materials (e.g. pre-transformed and/or transformed) compriseelements (e.g. chromium) which materials have a different vapor pressurein their elemental state (e.g., metallic state) relative to their oxidestate. When a pre-transformed material is being transformed, the element(as part of the pre-transformed material), may evaporate and/or formplasma. The evaporated material and/or its plasma may chemically react.The chemical reaction may comprise oxidation (e.g. form an oxide). Thechemical reaction may comprise reacting with a gas (e.g., in theenclosure). The chemical reaction may comprise reacting with a residualchemical (e.g., in the enclosure). The chemical reaction may comprisereacting with oxygen (e.g., molecule or radical). The chemical reactionmay comprise reacting with an oxygen and/or water molecule. Theevaporation and/or plasma formation of such (e.g., metallic) material,as well as its (e.g., subsequent) condensation and/or chemical reaction,may lead to generation of debris (e.g. in the form of soot). Withoutwishing to be bound to theory, the generation of debris may be a resultof condensation and/or chemical reaction (e.g., oxidation). At times,the reaction product of the material may have a higher vapor pressurerelative to its respective elemental state. For example, the oxide ofthe element may have a higher vapor pressure relative to its respectiveelemental state. At times, the material at its elemental state will tendto evaporate and/or form plasma quicker than its respective reactionproduct (e.g., oxide). Material examples comprise Molybdenum orTungsten, which have a low vapor pressure in their elemental state(e.g., metallic) as compared to their respective oxides. Metal maycomprise an elemental metal or metal alloy.

To reduce (e.g., avoid) evaporation and/or plasma formation of materials(e.g., and thus formation of debris) the temperature of the heated area(e.g., by the energy beam) may be controlled using a controller (e.g.comprising a GPU, CPU, FPGA or any other such computing element, e.g.,as described herein). FIG. 25 shows a schematic example of a system foradjusting a temperature of a heated area 2550 using a controller 2540(e.g. a control system, e.g., as shown in FIG. 24). The heated area(e.g., a melt pool) may be in the material bed (e.g., 2560), and/or on atarget surface. The heated area may comprise a portion of the exposedsurface of the material bed. The temperature of the heated area (e.g., alocation of the transformation) may be monitored using one or moresensors 2530 (e.g., optical sensors, and/or thermal sensors). In someexamples, the monitored temperature is compared (e.g., by thecontroller) to a predetermined threshold temperature value (or range) asa control parameter. The predetermined threshold value may be providedby a feed forward control element (e.g., 2505). The control parametermay comprise a specific location, and/or a specific time, of thetransformation. As the monitored temperature deviates from thepredetermined threshold value (or range), the temperature may beadjusted (e.g. using a feed-back control) to alter (e.g., reduce) thetemperature deviation. In an analogous manner to the temperatureadjustment, the power of the energy source generating the energy beam,and/or at least one characteristic of the energy beam (e.g., powerdensity thereof) may be adjusted additionally or alternatively thereto.

In some examples, the control comprises a closed loop control. Theclosed loop control may comprise a feedback, or feed-forward control.The control variable (e.g. power per unit area) of the energy beam(e.g., 2515) may be adjusted, e.g., by adjusting the energy source(e.g., 2510) parameters (e.g., by the controller). The control variable(e.g. power per unit area) of the energy beam may be pre-programmed.Pre-programing may be for a particular path of the energy beam. In someembodiments, both feed forward and feedback control may be used incombination. The control variable (e.g. power per unit area) of theenergy beam may be adjusted locally. Locally may refer to a particularheated area, adjacent to a particular heated area, a hatching within apath, a path of the energy beam, or a layer. The control variable (e.g.temperature) may be controlled by a closed loop control (e.g., 2545).The control may rely on the temperature measurements (e.g., by the oneor more sensors).

The control may comprise pre-defining a value, or a set of values, forthe control variable (e.g. power per unit area profile, power profile,and/or a temperature profile). The control variable may be pre-definedfor one or more transformation locations on the target surface. Thecontrol may comprise controlling the control variable (e.g. temperature,power, and/or power per unit area) in relation to a transformationlocation, in real time. Controlling may comprise regulating, monitoring,modulating, varying, altering, restraining, managing, checking, and/orguiding. Real time may be during transforming at least a portion of amaterial within the energy beam footprint, hatch, path, or slice. Realtime may be during the formation of the 3D object or portion thereof. Insome embodiments, the control may comprise adjusting (e.g. correcting)for at least one deviation of the temperature at the heated area, powerof the energy source generating the energy beam, and/or power per unitarea of the energy beam directed to the heated area. The adjustment maybe relative to a pre-defined power, power per unit area (e.g., valueand/or profile), or temperature (e.g., value and/or profile) at theheated area respectively. The feed forward controller may pre-identifyone or more locations at the (virtual) model of the requested 3D objectthat may be more challenging to correct using feedback control (e.g.U-turns, long hatches, and/or short hatches). The pre-identificationlocations (e.g., and operation) may comprise performing geometryanalysis of a 3D printing model associated with the desired 3D object.The printing model may comprise an OPC of the desired 3D object.

In some embodiments, the control comprises generating a physical model.In some embodiments, the control-model comprises the physical model. Insome embodiments, the computer-model comprises the physical model. Insome embodiments, the control-model excludes the physical model. In someembodiments, the computer-model excludes the physical model. Thephysical model may imitate and/or be analogous to a thermo-mechanicalmodel (e.g., of the 3D printing). The physical model may comprise one ormore elements that represent (e.g., are analogous to, or imitate) one ormore physical properties (e.g., heat profile of an energy beam, thermalhistory of an energy beam, dwell time sequence of an energy beam, powerprofile over time of an energy beam, energy beam distribution (i.e.,spot size)) associated with one or more components involved in theprocess of building a 3D object (e.g., energy beam, pre-transformed, ortransformed material). The physical model may be used to pre-determineone or more target parameters (e.g., a temperature threshold at one ormore points on the target surface, a power density of the energy beam, aFLS of the energy beam footprint on the target surface, a focus of theenergy beam footprint, a dwell time of the energy beam, an intermissiontime of the energy beam).

In some embodiments, the physical model is a complex model. The complexmodel may include a high order model (e.g., a high dimensionmathematical model, and/or a high polynomial order model). Highdimension refers to a dimension that is greater than one. For example, amathematical polynomial with a power of two, three, four, or more. Thecomplex model may comprise information related to (i) one or moremetrological properties of the forming 3D object (or portion thereof),(ii) physical properties of the pre-transformed and/or transformedmaterial, or (iii) thermal properties of the energy beam (e.g., along atleast a portion of the path used for building a 3D object). The complexmodel may include properties associated with more than one dimension ofthe 3D object. The complex model may include properties related to oneor more layers of the 3D object (e.g., previously formed and/or to beformed layers). The complex model may include geometry parameters (e.g.,contours, curves, slices) of the requested 3D object to be build. Thecomplex model may include one or more prediction models. The predictionmay pertain to the way at least a portion of the 3D object is hardenedduring and/or subsequent to the transformation of the pre-transformedmaterial which forms at least a portion of the 3D object. A predictionmodel may predict at least one physical property (e.g., thermal map ofthe 3D object) during its formation (e.g., during building one or morelayers of a 3D object), and/or a dwell time sequence of the energy beam(e.g., across one or more layers forming the 3D object).

In some embodiments, the physical model is a simplified (e.g., simple)model. A simplified model may include one or more properties related toat least a building portion of the 3D object (e.g., a single dimensionof the 3D object, or two dimensions of the 3D object). The simplifiedmodel may include one or more assumptions. The assumptions may comprisepre-determining values (e.g., assuming stable values) for one or moreproperties of the 3D object. The assumptions may include simplifying thegeometry of the 3D object (e.g., a single dimension of a portion of the3D object). The assumptions may include predicting at least one physicalproperty (e.g., temperature over time, temperature distribution withinat least a portion of the 3D object (e.g., over time), power density ofthe energy beam over time, heat profile of the material bed over time,and/or heat distribution within the material bed (e.g., over time)). Thesimplified model may be a discretized version of the complex model(e.g., may include predictions for a portion of the geometry of the 3Dobject). The simplified model may be a subset of the complex model(e.g., may include a single property). The complex model may comprise aplurality of simplified models.

In some embodimetns, the physical model is represented by an analogousmodel (e.g., an electrical model, an electronic model, and/or amechanical model). FIGS. 27A-27B illustrate examples of an electricalanalogous model. FIG. 27A illustrates an example of a simplifiedelectrical analogous model (e.g., a first order of complexity model).The electrical model may include one or more basic elements, forexample, a current source (e.g., FIG. 27A, 2760), a resistor (e.g., FIG.27A, 2768), a capacitor (e.g., FIG. 27A, 2777), an inductor, and/or aground component (e.g., FIG. 27A, 2784). The basic elements mayrepresent one or more physical properties of building a 3D object. Attimes, the basic elements may represent one or more components of the 3Dprinter. For example, the energy beam may be represented by a currentsource. In some examples, the angle of at least a portion of the 3Dobject (e.g., an overhang thereof) may affect the capacitance and/orresistor values representing a point on the edge of that at least aportion of the 3D object (e.g., this overhang). For example, the largerthe overhang angle with respect to the target (e.g., exposed) surface(e.g., the stepper the overhang), the smaller the resistor will be inthe physical-model, and the larger the capacitance in thephysical-model. The value of at least one resistor and/or capacitancemay be related to (i) the discretization distance and/or (ii) thefundamental material properties forming the 3D object. Thediscretization distance may be the physical length of a unit element(e.g., electrical element) which is represented by the basic discreteelements. The fundamental material properties of the build material maycomprise the thermal conductivity, the heat capacity, or the density ofthe build material (e.g., material forming the 3D object). In someexamples, the measured voltage probe points (in the physical-model),such as 2765, represent a measurement of the surface temperature (in theforming/formed 3D object). Closed loop and/or feedback control may bemodeled by a change of the current source as a response to a change inthe measured voltage, at the probe point (e.g., 2765). The model canalso predict the measured voltages (e.g., that can represent measuredtemperature). Measuring the temperature levels during the build and/orcomparing them to the modeled voltage, may allow (i) a (e.g.,systematic) study of the error in the physical-model, (ii) fine tuningof the model, (iii) finding a relationship between the physical processof 3D printing and the (e.g., simplified) physical-model representingit, or (iv) any combination thereof The voltage may be measured at theintersection of the current source and the branch of a resistor and/orcapacitor (e.g., FIG. 27A, 2765). The simplified (e.g., reduced) modelmay not be limited to simple and/or constant value components. As anexample, the capacitors and/or resistors can depend on the voltage C(V)and/or R(V) respectively. Additional components that can be used are,for example, current multiplier. The value of the current multiplier canrepresent in the physical-model a change in the absorption efficiency ofthe energy beam by the material in the 3D printing. For example, as thevalue of the current multiplier can depend on the voltage (imitating thephysical property of the absorption that can depend on the temperature).The voltage may be used to simulate a dependence (e.g., a temperature)of the capacitor and/or the resistor (e.g., C(V), and/or R(V)). Theanalogous model may include input from at least one sensor and/ordetector. The sensor and/or detector may detect a physical property ofat least one position on the target surface (e.g., temperature of aposition at the target surface, power of the energy beam, and/or thermalmap of the path of the energy beam). The sensor input may be fed intoone or more branches of the physical model.

In some embodiments, the physical model comprises an analog or digitalmodel. The model may comprise an electronic model. The model maycomprise a basic element. The basic element may be an electrical (e.g.,electronic) element. The electrical element may comprise active,passive, or electromechanical components. The active components maycomprise a diode, transistor, an integrated circuit, an optoelectronicdevice, display device, vacuum tube, discharge device, or a powersource. The passive components may comprise a resistor, a capacitor, amagnetic (inductive) device, a memristor, a network, a transducer, asensor, a detector, an antenna, an oscillator, a display device, afilter (e.g., electronic filter), a wire-wrap, or a breadboard. Theelectromechanical components may comprise a mechanical accessory, a(e.g., printed) circuit board, or a memristor. The basic elements may bevariable devices and/or have a variable value (for example, a variableresistor, and/or a variable capacitor). The resistor may be a linearresistor, non-linear resistor, carbon composition resistor, wire woundresistor, thin film resistor, carbon film resistor, metal film resistor,thick film resistor, metal oxide resistor, cermet oxide resistor,fusible resistor, variable resistor, potentiometer, rheostat, trimmer,thermistor, varistor, light dependent resistor, photo resistor, photoconductive cell, or a surface mount resistor. The capacitor may be aceramic, film, paper, polarized, non-polarized, aluminum electrolytic, atantalum electrolytic, niobium electrolytic, polymer, double layer,pseudo, hybrid, silver, mica, silicon, air-gap, or a vacuum capacitor.The inductor may be an air core inductor, ferro magnetic core inductor,iron core inductor, ferrite core inductor, toroidal core inductor,bobbin based inductor, multi layer inductor, thin film inductor, coupledinductor, plastic molded inductor, ceramic molded inductor, powerinductor, high frequency inductor, radio frequency inductor, choke,surface mount inductor, or a laminated core inductor. The physical modelmay be incorporated in a processor (e.g., computer). The physical modelmay comprise a circuit analog (e.g., in a processor). For example, thephysical model may comprise a virtual circuit analog. The physical modelmay comprise a tangible circuit. The physical model may comprise acircuit board. The circuit boards may comprise the one or moreelectrical elements.

FIG. 27B illustrates an example of a more complex electrical analogousmodel (e.g., a second order of complexity model) relative to the one inFIG. 27A. The more complex electrical analogous model may include one ormore basic electrical elements (e.g., a current source 2705, a resistor2720, a capacitor 2740, and/or a ground element 2745). The basic elementmay include a multiplier (e.g., a constant value represented in the FIG.27B, as “a” for the capacitor or “b” for the resistor). The multipliermay be variable. The multiplier may be adjusted. Adjustment may be donebefore, after, or during build of the 3D object (e.g., in real-time).Adjustment may be done manually and/or automatically (e.g., by acontroller). At times, the complex electrical analogous model may be(e.g., substantially) complete (e.g., include representation for alldimensions, and/or properties of a physical model of the 3D object).Substantially may be relative to the intended purpose of the 3D object.The complex (e.g., more complex) electrical analogous model may includeinput from one or more sensors and/or detectors. A sensor or detectormay sense or detect (respectively) a physical property of at least oneposition on the target surface (e.g., temperature of the target surface(e.g., temperature distribution thereof), power density of the energybeam, thermal map of the path of the energy beam, thermal map of theforming 3D object, and/or thermal map of the material bed). Thesensor/detector input may be fed (e.g., FIG. 27B, 2710, 2715, 2725) intoone or more branches (e.g., FIG. 27B, 2730) of the analogous electricalmodel (for example, a single branch may receive input from a singlesensor, a single branch may receive input from more than one sensor, ormultiple branches may receive input from a single sensor). The one ormore sensor inputs may provide an (e.g., substantially) accuratemeasurements of the process of building the 3D object. The sensor inputmay use a signal sensed using at least one optical fibers (e.g., fiberbundle). An example for at least one fiber (e.g., fiber bundle) that isconnected to a sensor/detector is described in Provisional PatentApplication Ser. No. 62/442,896, filed on Jan. 5, 2017, titled “OPTICALCALIBRATION IN THREE-DIMENSIONAL PRINTING” that is incorporated hereinby reference in its entirety.

In some embodiments, the measurements (e.g., thermal, or power density)based on the sensor/detector input are detailed (e.g., accuratemeasurements from one or more sensors, smaller number of assumptionsthan a first order complexity model). The detailed measurements mayallow observation of complex physical properties (e.g., diffusion of theheat through the forming 3D object and/or material bed). Detailed (e.g.,accurate, and/or pertaining to more than one physical property)adjustments may be made based on the detailed measurements. The detailedadjustments may minimize uncertainties (e.g., uncertainties related toassumptions of physical properties, uncertainties such as location ofthe energy beam, uncertainties related to temperature profile of theenergy beam, uncertainties related to geometry of the forming 3Dobject). The adjustments may be done by a controller. The analogousmodel (e.g., physical model) may act as a state observer. The analogousmodel may provide one or more measurements to the controller. Based onthe measurements, the controller may adjust one or more components ofthe 3D printer. For example, the controller may adjust one or morecharacteristics of the energy beam. The controller may adjust one ormore physical properties (e.g., electrical charge, e.g., position of anoptical element). Adjustment may be done before, after and/or during 3Dprinting. The controller may be a part of a processing (e.g., computer)system. The controller may comprise a processor. The controller may beany controller described herein. The processor and/or processing systemmay be any computer and/or computer system described herein.

In some examples, one or more sensors/detectors are used to sense/detect(respectively) one or more physical parameters within the 3D printersystem. Sensing and/or detecting may be done in real time (e.g., duringbuild of the 3D object). Sensing and/or detecting may be done offline(e.g., before and/or after building the 3D object). The sensor may beany sensor described herein. The detector may be a detector array. Thesensor and/or detector may be coupled to an optical fiber. A detectorarray and/or sensor array may be coupled to an optical fiber bundle.Various sensors and/or detectors can be found in Provisional PatentApplication No. 62/430,723 titled “OPTICS, DETECTORS, ANDTHREE-DIMENSIONAL PRINTING”, that was filed on Dec. 6, 2016, which isincorporated herein by reference in its entirety. The sensor and/ordetector may sense and/or detect (respectively) one or more physicalparameters of at least one layer of a forming 3D object. The sensorand/or detector may be translatable (e.g., movable, e.g., attached to agimbal). The sensor and/or detector may move back and forth (e.g., alonga path of an energy beam). The movement may be controlled (e.g.,manually or automatically, e.g., using a controller).

FIGS. 30A-30E illustrate an example of retro scan. A retro scan mayinclude moving the irradiated energy back and forth in the same generalplane (e.g., of the target surface) along a path (e.g., line). Movingthe irradiated energy may include moving one or more steps in theforward direction. The steps may be continuous or discontinuous. Thesteps may be isolated. For example, the steps may be tiles (e.g.,overlapping or non-overlapping tiles). For example, FIG. 30A illustratesan example of moving the irradiated energy (e.g., 3015) in six steps(e.g., 3010) in a forward direction (e.g., 3020) on a target surface(e.g., 3005) along a line. FIG. 30B illustrates an example of moving theirradiated energy (e.g., 3035) four steps (e.g., 3030) in a backwarddirection (e.g., 3040) on the target surface (e.g., 3025) along theline. FIG. 30C illustrates an example of moving the irradiated energybeam (e.g., 3055) six steps (e.g., 3050) in the forward direction (e.g.,3060), on the target surface (e.g., 3045) along the line. In the retroscan procedure, the operation illustrated in FIG. 30A is executed,followed by the operation illustrated in FIG. 30B, which is subsequentlyfollowed by the operation in FIG. 30C. Moving the irradiated energy mayinclude moving one or more steps selected from (i) moving in a forwarddirection to form a first forward path, (ii) irradiating to at leastpartially overlap the first forward path in a backwards direction toform a backwards path, and (iii) irradiating to at least partiallyoverlap the backwards path in a forward direction. Operations (i) to(iii) can be conducted sequentially. In some embodiments, the backwardspath overlaps the first forward path (at least) in part. In someembodiments, the second forward path overlaps the backwards path (atleast) in part. Moving the energy beam may include overall moving in theforward direction (e.g., two steps forward and one step backward). Forexample, when the non-overlapping second forward path exceeds the firstforward path in the direction of forward movement (e.g., differencebetween positions 7-8 on the target surface irradiated at time 15-16 inFIG. 30E). For example, FIG. 30D illustrates an example of moving theenergy beam in three iterations, which circles (e.g., 3080) show anexpansion of a superposition of irradiated positions on the targetsurface 3065. In the first iteration, the energy beam moves six steps inthe forward direction (e.g., 3080). In the second iteration, the energybeam moves four steps in the backward direction (e.g., 3075) from theprevious iteration. In the third step, the energy beam moves six stepsin the forward direction (e.g., 3070) from the earlier iteration, thusoverall moving eight steps in the forward direction on the targetsurface (e.g., 3025). In the illustrated example, the earliestirradiation position (e.g. first step) is indicated by the darkest graycircle. The shades of gray are lightened to indicate the subsequentsteps (from the earliest to the most recent irradiated position, e.g.,step two to step six) in the iteration, and the last irradiationposition is indicated by a white circle. FIG. 30E illustrates thegraphical representation of the retro scan, wherein the graphicalrepresentation illustrates the position of the irradiated energy on thetarget surface (e.g., 3085. E.g., position along an X axis) as time(e.g., 3090) progresses. The retro scan may be performed with thetransforming energy beam having an elliptical (e.g., circular) crosssection. The retro scan may be performed with the transforming energybeam having an oval (e.g., Cartesian oval) cross section. The retro scanmay be performed continuously (e.g., during the 3D printingtransformation operation, or a portion thereof). The retro scan may beperformed during printing of the 3D object. The movement of the energybeam may be controlled statically (e.g., before or after printing of the3D object). The movement of the energy beam may be controlleddynamically (e.g., during printing of the 3D object). The retro scan canbe performed with any cross section of the irradiated energy (e.g.,transforming energy) disclosed herein. For example, the retro scan canbe performed using a circular cross sectional energy beam (e.g.,focused, defocused; having small or large FLS), or an elliptical crosssectional energy beam (e.g., using the astigmatism mechanism). Theenergy beam used for the retro scan can be any transforming energy beamdisclosed herein (e.g., focused, defocused; having small or large FLS).

In some embodiments, the layer of hardened material (as part of the 3Dobject) is formed with a scanning energy beam, tiling energy beam, orany combination thereof The tiling energy beam can have a cross sectionthat is larger than the scanning energy beam. Larger may be by at leastabout 1.5*, 2*, 5*, 10*, 25*, 50*, or 100*. The symbol “*” designatesthe mathematical operation “times.” The scanning energy beam may have apower per unit area that is larger than the power per unit area of thetiling energy beam. The tiling energy beam may have a dwell time that islonger than the one of the scanning energy beam. The scanning energybeam may form feature that have a smaller FLS as compared to thefeatures formed by the tiling energy beam. FIG. 31 shows an example of alayer 3120 that is at least a part of a 3D object. The layer is formedusing a tiling energy beam that form tiles (e.g., 3123), and a scanningenergy beam that form hatches (e.g., 3122) and a rim (e.g., 3121). FIG.33 shows an example of a 3D printer comprising a build module 3350 and aprocessing chamber comprising atmosphere 3326. The 3D printer 3300comprises a scanning energy source 3321 generating a scanning energybeam 3301 that travels through a scanner 3320, through an optical window3315 to transform a portion of a material bed 3304 to a transformedmaterial 3317 (e.g., to form a 3D object).The 3D printer 3300 comprisesa tiling energy source 3322 generating a tiling energy beam 3308 thattravels through a scanner 3314, through an optical window 3335 totransform a portion of a material bed 3304 to a transformed material3317 (e.g., to form a 3D object). The 3D printer may comprise one ormore energy sources. The energy source may generate one or more energybeams. The energy beams may travel through the same or different opticalwindow. The energy beams may be directed by the same or differentscanners. Tiles may be formed by a (e.g., substantially) stationarytiling energy beam, which periodically moves along a path (e.g., path oftiles). The tiling energy beam may be of a lower power density than thescanning energy beam. Hatches may be formed by a continuously movingscanning energy beam. The dwell time of the tiling energy beam at aposition of the target surface that forms the tile, may be longer thanthe dwell time of the scanning energy beam at a positon of the targetsurface which forms the hatch. The cross section of the tiling energybeam may be larger than the cross section of the scanning energy beam.

At times, a single sensor and/or detector may be used to sense and/ordetect (respectively) a plurality of physical attributes (e.g.,parameters), for example, power density over time of an energy beam,temperature over time of an energy beam, and/or energy source power overtime. At times, a single pixel sensor and/or detector may be used tosense and/or detect (respectively) a physical attribute (e.g., powerdensity (e.g., over time) of an energy beam, temperature (e.g., overtime) of an energy beam, and/or energy source power (e.g., over time).FIG. 28A shows an example of irradiating an energy beam at threepositions X₁, X₂ and X₃. The irradiations at the positions may formthree melt pools. The irradiations at the position may form three tiles.The irradiations at the portions may be by a non-oscillating energy beam(e.g., traveling along path 2825). The irradiation may be by anoscillating (e.g., retro scanning, dithering) energy using an energybeam that travels along an oscillating path, 2820. The energy beam canbe the transforming energy beam. For example, the energy beam can be atiling energy beam. A position of the energy beam (e.g., FIG. 28A, 2810)may be measured as a function of time (e.g., FIG. 28A, 2815), e.g., asthe oscillating (e.g., retro scan) energy beam performs oscillations2820, or as the non-oscillating energy beam travel along its path 2810.The oscillating energy beam can perform oscillations that comprise aback and forth movement along the path of the non-oscillating energybeam. The oscillations can have an amplitude that is equal to, orsmaller than, a melt pool diameter. The oscillations can have anamplitude that is equal to, or smaller than, a melt pool diametersmaller than the diameter of the cross section of the energy beam. Ascompared to the non-oscillating energy beam (e.g., 2825), irradiating atposition X₁ during the period t₁-t₂, the oscillating beam (e.g., 2820)travels back and forth between X_(1−d) and X_(1+d), as shown in theexample of FIG. 28A. FIG. 28B illustrates an example that depictstemperature measurements 2830 as a function of time 2835, while formingtiles (e.g., having center positions FIG. 28A, X₁, X₂ and X₃). In theexample shown in FIG. 28B, during the spatial oscillations of the energybeam (e.g., 2820), the temperature measured 2840 that is emitted fromthe target surface at the footprint of the energy beam, oscillates aswell. As the footprint of the oscillating energy beam at the targetsurface physically oscillates between the center of the area that isheated by the energy beam (e.g., FIG. 28A, X₁, e.g., tile center) andthe outskirts of that center (e.g., FIG. 28A, X_(1−d), or X_(1+d), e.g.,tile outskirts), the measured temperature emitted from the targetsurface at the footprint fluctuate between a maximum temperature value(e.g., at the tile center) and a minimum temperature value (at the tileoutskirts). FIG. 28B shows temperature measurement profile 2845 as afunction of time, of a non-oscillatory energy beam that travels alongpath 2825 (in FIG. 28A), during t₁ to t₂. In the example shown in FIG.28B, the power stays (e.g., substantially) constant during the periodfrom t₁ to t₂. FIG. 28D illustrates an example that depicts temperaturemeasurements 2880 as a function of time 2885, while forming a tile thatis centered at X₁ (in FIG. 28A). In the example shown in FIG. 28D,during the spatial oscillations of the energy beam, the measuredtemperature from the target surface at the footprint of the energy beamoscillates as well 2850. As the oscillating energy beam footprint at thetarget surface physically oscillates between the center of the areaheated by the energy beam (e.g., FIG. 28A, X₁, e.g., tile center) andthe outskirts of that center (e.g., FIG. 28A, X_(1−d), or X_(1+d), e.g.,tile outskirts), the measured temperature from the target surface at theenergy beam footprint 2850 fluctuates between a local maximumtemperature value (e.g., at the tile center) and a minimum temperaturevalue (at the tile outskirts). FIG. 28B shows temperature measurementprofile 2855 as a function of time, of a non-oscillatory energy beamthat travels along path 2825 during t₁ to t₂. In the example shown inFIG. 28B, the power 2857 of the energy source that generates the energybeam is kept (e.g., substantially) constant during the period from t₁ tot_(1+d), until the temperature approaches a (e.g., predetermined) valueof T₄; and decreases in order to keep the temperature at a (e.g.,substantially) constant value T₄ during the period from t_(1+d) to t₂.One or more detectors may measure the temperature distribution along thepath (e.g., of the scanning and/or non-scanning energy beam), bydetecting the temperature. The speed (e.g., moving speed) and/oramplitude of the backwards and forwards movements of the oscillatingbeam can be (e.g., substantially) similar or different with respect toeach other. The speed and/or amplitude of at least two of the forwardsmovements of the oscillating beam may be different along the path. Thespeed and/or amplitude of at least two of the backwards movements of theoscillating beam may be (e.g., substantially) similar along the path.

In some embodiments, the footprint of the oscillation energy beam on thetarget surface translates back and forth around a position of the targetsurface (e.g., center of the tile). The amplitude of the oscillation maybe smaller than, or equal to the FLS (e.g., diameter) of a tile. In someembodiments, at least one characteristic of the energy beam is held at a(e.g., substantially) constant value using close loop control during theoscillation, using a measured value (e.g., of the same, or anothercharacteristics). For example, the power of the energy source thatgenerates the energy beam may be held at a constant value, usemeasurements of temperature at one or more locations at the targetsurface (e.g., at a location and/or as the energy beam travels along thepath). For example, the temperature at the irradiation location (e.g.,energy beam footprint) is held at a (e.g., substantially) constantmaximum value (e.g., using a controller), and the power of the energysource generating the energy beam is measured and/or observed. Thetemperature may be held at a constant maximum value by altering thepower of the energy source. The energy source power may be held at aconstant value, resulting in an alteration of the temperature at thetarget surface location of the energy beam footprint. The areal extentof the heated area may be extrapolated from (e.g., fluctuations of) thepower and/or temperature measurements. The heated area may comprise amelt pool (e.g., FIG. 26A, 2605) or its vicinity (e.g., 2610). In someembodiments, the oscillating energy beam that is held in closed loopcontrol may facilitate controlling at least one characteristic of themelt pool (e.g., temperature and FLS). In some embodiments, thevariation in power of the energy beam may be cycling and/or may dropduring the irradiation of the energy beam (e.g., during the 3D printing)at the target surface. FIG. 28C illustrates an example method ofmeasuring power (e.g., 2860) of the energy source as a function of time(e.g., 2865), e.g., using a single sensor/detector. In this examplemethod, a threshold temperature (e.g., temperature to be maintained atthe target surface) may be specified. The threshold temperature may bekept (e.g., substantially) constant. The sensor/detector may monitor thetemperature at discrete time points. The control system may adjust atleast one characteristic of the energy source generating the energy beam(e.g., its power) to maintain the threshold temperature by comparing amonitored temperature to the threshold temperature. The control systemmay adjust at least one characteristic of the energy beam to maintainthe threshold temperature by comparing a monitored temperature to thethreshold temperature. For example, the control system may adjust thepower of the energy source and/or the power density of the energy beamto maintain the threshold temperature by comparing a monitoredtemperature to the threshold temperature. Thus, the power over time mayvary to maintain a threshold temperature value. FIG. 28C illustrates anexample of varying power over time, as the energy beam spatiallyoscillates (FIG. 28A, 2820) over time in the period from t₁ to t₂. Thepower over time may be cyclic and dropping over time (e.g., 2875 and2870) to maintain a constant temperature value of an oscillating energybeam during the period from t₁ to t₂. FIG. 28D shows an example of boththe power profile over time 2857 and its respective temperature provideover time 2855 of a non-oscillating energy beam, that aims to maintainthe temperature value at T₄. At times, one or more physical properties(e.g., melt pool characteristics) of the target surface may be sensedand/or detected by a single sensor and/or detector respectively. Forexample, the control system may adjust the at least one characteristicof the energy beam and/or energy source by comparing (i) a monitoredtemperature to the threshold temperature, (ii) a monitored power densityto a threshold power density, (iii) a monitored power to a thresholdpower, (iv) or any combination thereof The power may be of the energysource that generates the energy beam. The power density may be of theenergy beam. The temperature may be of a position at the target surface(e.g., at the footprint of the energy beam).

The reduction of debris may allow reducing use of (e.g., eliminate) atleast one mechanism that maintains the 3D printer (or any of itscomponents) at a reduced debris level (e.g., free of debris). Forexample, the reduction of debris may reduce (e.g., eliminate) theutilization of an optical window (e.g., FIG. 1, 115) cleaning mechanism.

The hardened material (e.g., 3D object) may have a porosity of at mostabout 0.05 percent (%), 0.1% 0.2%, 0.3%, 0.4%, 0.5%, 0.6%, 0.7%, 0.8%,0.9%, 1%, 2%, 3%, 4%, 5%, 6%, 7%, 8%, 9%, 10%, 20%, 30%, 40%, 50%, 60%,70%, or 80%. The hardened material may have a porosity of at least about0.05 percent (%), 0.1%, 0.2%, 0.3%, 0.4%, 0.5%, 0.6%, 0.7%, 0.8%, 0.9%,1%, 2%, 3%, 4%, 5%, 6%, 7%, 8%, 9%, 10%, 20%, 30%, 40%, 50%, 60%, 70%,or 80%. The hardened material may have a porosity between any of theafore-mentioned porosity percentages (e.g., from about 0.05% to about0.2%, from about 0.05% to about 0.5%, from about 0.05% to about 20%,from about from about 0.05% to about 50%, or from about 30% to about80%). In some instances, a pore may transverse the formed object. Forexample, the pore may start at a face of the planar object and end atthe opposing face (e.g., bottom skin) of the hardened material. The poremay comprise a passageway extending from one face of the planar objectand ending on the opposing face of that hardened material. In someinstances, the pore may not transverse the formed object. The pore mayform a cavity in the formed 3D object. The pore may form a cavity on aface of the formed 3D object (e.g., the face of the 3D object). Forexample, pore may start on a face of a 3D plane and not extend to theopposing face of that 3D plane. The first formed layer of hardenedmaterial in the 3D object may be referred to herein as the “bottomskin.” The term “bottom skin” may also refer to the first form layer(e.g., bottom most layer) of a hanging structure or cavity ceiling.

In some embodiments, the control may be effectuated by at least onecontroller (e.g., as disclosed herein). The controller may control theenergy beam, and/or sensor(s) (e.g., gas sensor). The controller maycontrol the enclosure comprising its pressure, humidity, oxygen, ortemperature. The controller may control safety related parameters,systems and/or apparatuses (e.g., interlocks, and/or load locks). Theinterlocks and/or load locks may separate the processing chamber (e.g.,comprising atmosphere 2926) from the build module (e.g., Fir. 29, 2940).The controller may control the “health” (e.g., proper operation) of thesystem(s) and/or apparatus(es). The controller may control thedesignated (e.g., proper) operation of the system and/or apparatuses(e.g., their proper movement (e.g., jam, or flow), any gas leak, and/orpower stability). The controller may control a connection tocommunication systems (e.g., internet). The controller may comprise twoor more processors that are connected via the cloud (e.g., internet).The controller may alert of any errors in storing information, logging,imaging, process signals, or any combination thereof. The controller maycomprise a user interface software. The software may be a non-transitorycomputer-readable medium (e.g., in which program instructions arestored). The controller may control the system and/or apparatuses (e.g.,in real time). For example, the controller may control (e.g., operate,and/or regulate) the system and/or apparatuses in test and/or 3D printmode. The controller may control one or more 3D printing parameters. Thecontroller may save and/or load files. The controller (e.g., softwarethereof) may identify portions of the desired object that are difficultto build (e.g., cannot be built). The controller may recommend a schemeto design around printing of difficult portions. The controller mayrecommend an alternate design scheme for the 3D printing. The controller(e.g., software) may perform a risk evaluation of 3D objects (orportions thereof). The controller (e.g., software) may comprisevisualization of the slicing, and/or hatching scheme (e.g., in realtime, before printing the 3D object, and/or after printing the 3Dobject). The systems and/or apparatuses may effectuate visualization ofthe printed 3D object (e.g., in real-time, before printing the 3Dobject, and/or after printing the 3D object). The visualization maycomprise the manner in which the layers of hardened material are goingto be formed from their respective (e.g., virtual) slices. Thecontroller (e.g., software thereof) may evaluate (e.g., check for) anyerrors in the 3D printing process. The controller (e.g., software) mayevaluate (e.g., check for) any deviations of the 3D object from thedesired (e.g. requested) 3D object. The evaluation may be before,during, and/or after formation of the 3D object. The evaluation may bereal-time evaluation during the 3D printing process. The controller maycontrol the energy beam, temperature of at least one position of theexposed surface of the material bed, temperature of at least oneposition of the interior of the material bed (e.g., based on apredictive model), or any combination thereof (e.g., in real time duringthe 3D printing process).

In some embodiments, the controller comprises one or more components.The controller may comprise a processor. The controller may comprise aspecialized hardware (e.g., electronic circuit). The controller may be aproportional-integral-derivative controller (PID controller). Thecontrol may comprise dynamic control (e.g., in real time during the 3Dprinting process). For example, the control of the (e.g., transforming)energy beam may be a dynamic control (e.g., during the 3D printingprocess). The PID controller may comprise a PID tuning software. The PIDcontrol may comprise constant and/or dynamic PID control parameters. ThePID parameters may relate a variable to the required power needed tomaintain and/or achieve a setpoint of the variable at any given time.The calculation may comprise calculating a process value. The processvalue may be the value of the variable to be controlled at a givenmoment in time. For example, the process controller may control atemperature by altering the power of the energy beam, wherein thetemperature is the variable, and the power of the energy beam is theprocess value. For example, the process controller may control a heightof at least one portion of the layer of hardened material that deviatesfrom the average surface of the target surface (e.g., exposed surface ofthe material bed) by altering the power of the energy source and/orpower density of the energy beam, wherein the height measurement is thevariable, and the power of the energy source and/or power density of theenergy beam are the process value(s). The variable may comprise atemperature or metrological value. The parameters may be obtained and/orcalculated using a historical (e.g., past) 3D printing process. Theparameters may be obtained in real time, during a 3D printing process.During a 3D printing process, may comprise during the formation of a 3Dobject, during the formation of a layer of hardened material, or duringthe formation of a portion of a layer of hardened material. The outputof the calculation may be the power of the energy source and/or powerdensity of the energy beam. The calculation output may be a relativedistance (e.g., height) of the material bed (e.g., from a coolingmechanism, bottom of the enclosure, optical window, energy source, orany combination thereof).

In some embodiments, the controller comprises a PID controller. The PIDcontroller (e.g., control algorithm) may comprise aproportional-integral controller (i.e., PI controller), deadband,setpoint step alteration, feed forward control, bumpless operation, PIDgain scheduling, fuzzy logic, or computational verb logic. The setpointmay be a target value (e.g., target temperature, target height of theexposes surface of the material bed, or target power of the energysource). In some embodiments, the controller may comprise a plurality ofsetpoints (e.g., that are of different types).

In some examples, the calculations may take into account historical data(e.g., of certain types of 3D object geometries), existing 3D structure(e.g., 3D object), future 3D portion of the desired 3D object to beprinted, or any combination thereof Future portion of the desired 3Dobject to be printed may comprise a portion of the 3D object that shouldbe printed later in time (e.g., a layer to be printed in the futureduring the 3D printing process of the desired 3D object). Thecalculations may utilize chemical modeling (oxides, chemicalinteraction). The chemical modeling may be used to understand the effectof various reaction products (e.g., oxides) and chemical interactions onthe 3D printing of a 3D object. For example, understanding a reducedwetting (e.g., lack thereof) due to oxidation of the layer. The 3Dprinting may utilize etching (e.g., plasma etching) to reduce the amountof oxides (e.g., oxide layer) on the forming 3D object. The etching maybe performed during the 3D printing.

In some embodiments, the setpoint is altered (e.g., dynamically).Altering the setpoint may comprise setpoint ramping, setpoint weighting,or derivative of the process variable. The bumpless operation maycomprise a “bumpless” initialization feature that recalculates theintegral accumulator term to maintain a consistent process outputthrough parameter changes. The control may comprise high sampling rate,measurement precision, or measurement accuracy that achieve(s)(individually or in combination) adequate control performance of themethod, system, and/or apparatus of the 3D printing. The control (e.g.,control algorithm) may comprise increasing a degree of freedom by usingfractional order of the integrator and/or differentiator.

In some embodiments, the controller comprises a temperature controller(e.g., temperature PID controller), or a metrology controller (e.g.,metrology PID controller). The controller may be a nested controller.Nested may be a first controller controlled within a second controller.For example, a temperature PID controller may comprise a metrology PIDcontroller. For example, a metrology PID controller may comprise atemperature PID controller. For example, a first temperature PIDcontroller may comprise a second temperature PID controller. Forexample, a first metrology PID controller may comprise a secondmetrology PID controller. The metrology controller may use input fromthe temperature controller and/or vice versa. The temperature controllermay receive input from the metrology detector (e.g., in case itcomprises a nested metrology controller) and/or from the temperaturedetector. The metrology detector may be also referred herein as a“metrological detector.” The temperature controller may consider anycorrective deformation. The temperature controller may consider objectpre-correction (OPC; e.g., FIG. 6). The nested controller mayincorporate data of corrective deformation (e.g., OPC), from themetrology detector, and/or from the temperature detector. The nestedcontroller may control the degree of deformation of the forming 3Dobject. The metrological detector and/or temperature detector (e.g., andcontroller) may resolve irregularities (e.g. of height less than about 1μm, 5 μm, 8 μm, 10 μm, 15 μm, 20 μm, 30 μm, or 40 μm) of a forming 3Dobject. The irregularities may comprise material bed irregularities,and/or height irregularities.

In some embodiments, a metrological detector is used in the control ofthe 3D printing. The metrological detector may include an imagingdetector (e.g., CCD, camera) to monitor irregularities. The imagingdevice (e.g., as disclosed herein) may comprise an imaging detector. Theimaging detector is also referred to herein as “image detector.” Theimage detector may comprise detecting an area of the forming 3D objectand convert it to a pixel in the X-Y (e.g., horizontal) plane. Theheight (Z-plane) of the area may be measured using one or more computeralgorithms (e.g. a phase shift algorithm). The algorithm may comprise a(e.g., digital) modulation scheme that conveys data by changing (e.g.,modulating) the phase of a reference signal (e.g., carrier wave). Theimaging detector may capture an area of a FLS of at least about 40 μm,50 μm, 60 μm, 70 μm, 80 μm, 90 μm, 100 μm, 200 μm, 500 μm, 1 millimeteror 2 millimeter. The FLS of the captured area by an imaging detector,may be between any of the afore-mentioned sizes (e.g., from about 40 μmto about 2 millimeter, from about 100 μm, to about 1 millimeter, fromabout 40 μm to about 70 μm, or from about 70 μm to about 80 μm). A pixel(X,Y) of the imaging detector may detect at least one FLS (e.g., alength or width) of at least about 40 μm, 50 μm, 60 μm, 70 μm, 80 μm, 90μm, 100 μm, 200 μm, 500 μm, 1 millimeter, 2 millimeter, 10 millimeter,20 millimeter, 50 millimeter, 100 millimeter, 200 millimeter, 250millimeter, 300 millimeter or 500 millimeter. At least one FLS (e.g.,length or width) of the captured area within a pixel of an imagingdetector, may be between any of the aforementioned FLS values (e.g.,from about 40 μm to about 200 millimeter, from about 100 μm, to about300 millimeter, from about 40 μm to about 500 millimeter, or from about100 to about 300 millimeter, from about 150 millimeter to about 170millimeter). The imaging detector may operate at a frequency of at leastabout 0.1 Hertz (Hz), 0.2 Hz, 0.5 Hz, 0.7 Hz, 1 Hz, 1.5 Hz, 2 Hz, 3 Hz,4 Hz, 5 Hz, 6 Hz, 7 Hz, 8 Hz, 10 Hz, 20 Hz, 50 Hz, 100 Hz, 200 Hz, 300Hz, 400 Hz, or 500 Hz. The frequency of the imaging detector, may bebetween any of the afore-mentioned frequencies (e.g., from about 0.1 Hzto about 500 Hz, from about 1 Hz to about 500 Hz, from about 1 Hz toabout 100 Hz, from about 0.1 Hz to about 100 Hz, from about 0.1 Hz, toabout 1 Hz, from about 0.5 Hz to about 8 Hz, or from about 1 Hz to about8 Hz). The metrological detector may perform positional detection. Toperform positional detection, the metrological detector may be mountedon a stage (e.g. elevator or calibration plates). The stage may bemovable, and/or controlled (e.g., manually and/or automatically; before,after, and/or during the 3D printing). Alternatively, or additionally,the metrological detector may receive metrology and/or calibrationinformation from one or more apparatuses of the 3D printer. The one ormore apparatuses may comprise the stage. natively or additionally, themetrological detector may use absolute calibration information. FIG. 20shows an example of a logical sequence used by the nested controller inwhich data from the object pre-print correction (OPC) procedure 2003 istaken into account by the metrology detector 2002, which in turn feedsits output to a temperature controller 2001 that operates in a closedloop control, and takes into account measurements of the temperaturecontroller. The OPC data may be (e.g., directly) taken into account bythe temperature controller and/or metrology controller. The nestedcontroller may incorporate a metrology controller and/or temperaturecontroller. The (e.g., nested) controller may consider OPC data.

In some embodiments, the control system uses data from the metrologicaldetector. The control system may use the data to control one or moreparameters of the 3D printing. For example, the control system may usethe metrology data to control one or more parameters of the layerdispensing mechanism (e.g., the material dispenser, the levelingmechanism, and/or the material removal mechanism). For example, themetrological measurement(s) may facilitate determination and/orsubsequent compensation for a roughness and/or inclination of theexposed surface of the material bed with respect to the platform and/orhorizon. The inclination may comprise leaning, slanting, or skewing. Theinclination may comprise deviating from a planar surface that isparallel to the platform and/or horizon. The roughness may compriserandom, or systematic deviation. The systematic deviation may comprisewaviness. The systematic deviation may be along the path of the materialdispensing mechanism (e.g., along the platform and/or the exposedsurface of the material bed), and/or perpendicular to that path. Forexample, the controller may direct the material dispenser to alter theamount and/or rate of pre-transformed material that is dispensed. Forexample, the controller may direct alteration of a target heightaccording to which the leveling mechanism planarizes the exposed surfaceof the material bed. For example, the controller may direct the materialremoval member to alter the amount and/or rate of pre-transformedmaterial that is removed from the material bed (e.g., during itsplanarization). The control system may use the metrology data to controlone or more parameters of the energy source and/or energy beam. The oneor more measurements from the metrological detector may be used to alter(e.g., in real time, and/or off line) the computer model. For example,the metrological detector measurement(s) may be used to alter the OPCdata. For example, the metrological detector measurement(s) may be usedto alter the printing instruction of one or more successive layers(e.g., during the printing of the 3D object).

In some embodiments, the detector and/or controller averages at least aportion of the detected signal over time (e.g., period). In someembodiments, the detector and/or controller reduces (at least in part)noise from the detected signal (e.g., over time). The noise may comprisedetector noise, sensor noise, noise from the target surface, or anycombination thereof The noise from the target surface may arise from adeviation from planarity of the target surface (e.g., when a targetsurface comprises particulate material (e.g., powder)). The reduction ofthe noise may comprise using a filter, noise reduction algorithm,averaging of the signal over time, or any combination thereof.

In some embodiments, the metrological detector is calibrated. Forexample, the metrological detector may be detected and/or calibrated insitu in the enclosure (e.g., in the processing chamber, e.g., comprisingatmosphere FIG. 29, 2926). The metrological detector may use astationary structure to calibrate at least one height position. Forexample, the metrological detector may use the floor of the processingchamber (e.g., FIG. 29, 2950) as a metrological (e.g., height) referencepoint. The metrological detector may use one or more positions at theside wall of the processing chamber as metrological reference point. Theprocessing chamber may comprise one or more reference stationary pointsthat are not disposed on the wall and/or floor of the processingchamber. For example, the processing chamber may comprise a stationaryruler comprising slits and/or steps at designated locations to be usedas reference point for metrological calibration.

FIG. 19 shows an example of a metrological detector (e.g., heightmapper) which projects a striped image on the exposed surface of amaterial bed (e.g., powder bed), which image comprises darker stripes1901 and lighter stripes 1902. The metrological detector may operateduring at least a portion of the the 3D printing. For example, themetrological detector can project its image before, after, and/or duringthe operation of the transforming energy beam. The projected image maycomprise a shape. The shape may be a geometrical shape. The shape may bea rectangular shape. The shape may comprise a line. The shape may scanthe target surface (e.g., exposed surface of the material bed)laterally, for example, from one side of the target surface to itsopposing side. The shape may scan at least a portion of the targetsurface (e.g., in a lateral scan). The scan may be along the length ofthe exposed surface. The projected shape may span (e.g., occupy) atleast a portion of the width of the target surface. For example, theshape may span a portion of the width of the target surface, the widthof the target surface, or exceed the width of the target surface. Theshape may scan the at least a portion of the target surface before,after and/or during the 3D printing. The scan may be controlled manuallyand/or automatically (e.g., by a controller). The control may be before,after and/or during the 3D printing. For example, the shape may scan theexposed surface before, after and/or during the operation of thetransforming energy beam. The shape may be detectable (e.g., using anoptical and/or spectroscopic sensor). The scanning energy beam maycomprise the shape. The projected shape may be of an electromagneticradiation (e.g., visible light). The projected shape may be detectable.The projected shape may scan the target surface at a frequency of atleast about 0.1 Hertz (Hz), 0.2 Hz, 0.5 Hz, 0.7 Hz, 1 Hz, 1.5 Hz, 2 Hz,3 Hz, 4 Hz, 5 Hz, 6 Hz, 7 Hz, 8 Hz, 10 Hz, 20 Hz, 50 Hz, 100 Hz, 200 Hz,300 Hz, 400 Hz, or 500 Hz. The projected shape may scan the targetsurface at a frequency between any of the afore-mentioned frequencies(e.g., from about 0.1 Hz to about 500 Hz, from about 1 Hz to about 500Hz, from about 1 Hz to about 100 Hz, from about 0.1 Hz to about 100 Hz,from about 0.1 Hz, to about 1 Hz, from about 0.5 Hz to about 8 Hz, orfrom about 1 Hz to about 8 Hz). The image may comprise (e.g.,alternating) stripes. The distance between the stripes may be constant.The distance between the stripes may be variable. The distance betweenthe stripes may be varied (e.g., manually or by a controller) in realtime. Real time may be when performing metrological detection. Real timemay be when building (e.g., printing) the 3D object. The deviation fromthe regularity (e.g., linearity) of the stripes may reveal a heightdeviation from the average (or mean) exposed surface (e.g., of thematerial bed) height. The material bed in the example of FIG. 19 is anInconel 718 powder bed. In the example shown in FIG. 19, a 3D object1905 is partially buried in the material bed, and lifts a portion of thepre-transformed material (e.g., powder) of the material bed such that adeviation from the linearity of the stripes is visible. The shape of thedeviation from regularity (e.g., linearity) may reveal a shapecharacteristics of the buried 3D object portion (that is buried in thematerial bed). For example, the lines above the 3D object 1904 are(e.g., substantially) linear, whereas the lines above the 3D object 1905curve. The deviated (e.g., curved) lines above a 3D object may relate toa warping of the 3D object (e.g., 1905) that is (immediately)underneath. The regularity (e.g., linearity) of the lines detected abovethe 3D object may relate to the planarity of the top surface of the 3Dobject (e.g., 1904) that is (immediately) underneath. For example, linesabove the 3D object (whether buried in the material bed, or exposed)that match the regularity of the projected image, may reveal a planartop surface of a 3D object. For example, a deviation from the regularityof the projected image above the 3D object (whether buried in thematerial bed, or exposed), may reveal a deformation in the top surfaceof a 3D object. For example, linear lines above the 3D object may reveala planar top surface of a 3D object, when the metrology projectorprojects stripes. For example, non-linear (e.g., curved) lines above the3D object may reveal a non-planar (e.g., curved) top surface of a 3Dobject, when the metrology projector projects stripes. The reflectivityof the target surface may indicate the planar uniformity of the exposedsurface. FIG. 19, 1903 shows a 3D object in a material bed, which 3Dobject is reflective, whereas the material bed is substantially lessreflective.

At times, formation of the 3D object by the 3D printing methodologycauses one or more portions of the 3D object to deform. The deformationmay comprise bending, warping, arching, curving, twisting, balling,cracking, dislocating, or any combination thereof The deformation mayoccur in the layer that is currently being generated. The deformationmay occur in at least a portion of the 3D object that was previouslybuild (e.g., as it hardens). The deformation may occur during the 3Dprinting. The previously build portion may be disposed within thematerial bed. For example, the portion may be buried in the materialbed. The portion may not be visible (e.g., optically) from the exposedsurface of the material bed. A displacement of the layer being built maybe visible (e.g., optically). The visibility may be direct using anoptical sensor (e.g., a camera). The camera may be a high-resolutioncamera. The visibility may be indirect (e.g., using a metrologicaldetector such as a height mapper (e.g., FIG. 19).

In some examples, temporary fixtures (termed herein as “flags”) assistin controlling (e.g., monitoring) a deformation that manifests itselfwithin the material bed, and is not visible by external means (e.g.,metrology and/or optical sensors). One or more fixtures may be attachedto one or portions of the 3D object that are susceptible to deformationwhile being disposed within the material bed. The one or more fixturesmay be temporary fixtures that may be removed after the 3D printing iscomplete. The fixtures may not be part of the requested 3D object. Thefixtures may be of the same material that the 3D object is formed from.FIG. 23A shows an example of a requested 3D object 2312 that is beingformed in a material bed 2314, which 3D object is disposed on a platform2310 and has a portion that is susceptible to deformation to which aflag 2313 is attached at position 2315. The flags may be formed duringthe 3D printing process. The flags may be formed as part of the 3Dprinting process of the 3D object. The flags may be printedsimultaneously with the printing of the 3D object. The flags may bedetachable. The flags may be a wire. The flag may have a FLS that issubstantially similar or smaller than the FLS of the portion of the 3Dobject to which it is attached. The top portion of the flag (e.g., tipof the flag, top most portion of the flag) may be visible by the opticaland/or metrological sensor. A displacement (e.g., movement) of the flagmay be caused by a displacement of the 3D portion to which it isattached. The displacement may be relative to an expected position ofthe flag (e.g., that is attached to a non-deformed 3D object portion). Adisplacement of the flag may be indicative of at least a movement of theportion of the 3D object to which it is attached. The movement (e.g.,from a position of its formation) may be due to a deformation (e.g.,during its hardening and/or softening). FIG. 23B shows an example of the3D object 2312 of FIG. 23A that is build up into the 3D object 2322,which is formed in a material bed 2324, which 3D object is disposed on aplatform 2320 and has a portion that is susceptible to deformation towhich a flag 2323 is attached at position 2325. As the 3D object 2312 isbuild up into 3D object 2322, the portion that is attached to the flagdeforms and moves both horizontally and vertically from position 2325 toposition 2326, resulting in a displacement of the flag from position2323 to position 2328. In the example shown in FIG. 23B, the tip of theflag 2328 protrudes from the exposed surface of the material bed and canbe detected optically.

The 3D object may be attached to the platform. FIG. 23A shows a 3Dobject that is attached to the platform 2310 at position 2311. The 3Dobject may not contact the platform. The 3D object may not be anchoredto the platform. The 3D object may float (e.g., anchorlessly) in thematerial bed. The 3D object may be suspended (e.g., anchorlessly) in thematerial bed. The 3D object may comprise auxiliary support(s) or may bedevoid of auxiliary support. The auxiliary support(s) may comprise theplatform and/or anchor(s) to the platform. The auxiliary support maycontact or not contact the platform. The auxiliary support may connector not connect to the platform. The object with the auxiliary supportmay float anchorlessly in the material bed. The material bed maycomprise flowable material during the 3D printing. The material bed maybe devoid of a pressure gradient during the 3D printing. The materialbed may be at ambient temperature and/or pressure during the 3Dprinting. Ambient temperature and/or pressure may comprise roomtemperature and/or pressure respectively.

In some embodiments, a method, system, apparatus, and/or software maycomprise an algorithm that predicts and/or identifies one or more pointson a surface of the desired 3D object surface that are susceptible(e.g., prone to) deformation (e.g., warp). The method, system,apparatus, and/or software may comprise generation direction (e.g.,printing instruction) and/or direct the formation (e.g., printing) ofthe flag structure connected to the portion of the 3D object that issusceptible to deformation. The portion may be a portion that isdisposed in the material bed. The portion may be a portion that is notdetectable by the sensor (e.g., optical, and/or metrological). Themethod, system, apparatus, and/or software may comprise calculating(e.g., computing) a “flag amplification ratio.” The flag amplificationratio may comprise a relation between the displacement of the flag andthe deformation of the (buried, covered, and/or hidden) 3D objectportion. The displacement may be horizontally and/or vertically (e.g.,in X, Y, and/or Z direction). The flag amplification ratio may indicatea relationship between the displacement of a detectable portion of theflag (e.g., tip of the flag) and the deformation of the (hidden) objectportion.

In some embodiments, the controller comprises a PID controller. Thecontroller may comprise a cascade control (e.g., usage of a multiplicityof PID controllers). The control may comprise using a multiplicity(e.g., two) PID controllers. The usage of the multiplicity of PIDcontrollers may yield better dynamic performance as compared to theusage of a single PID controller. The cascade control may comprise afirst PID controller that controls the setpoint of a second PIDcontroller. The first PID controller may be an outer loop controller.The second PID controller may be an inner loop controller.

At times, the controller samples the measured process variable. Thecontroller may perform computations (e.g., calculations) utilizing themeasured process variable. The controller may transmit a controlleroutput signal (e.g., resulting from the computation). The controller mayhave a loop sample time. The loop sample time may (i) comprise the timeat which the controller samples the measured process variable, (ii)perform the computation using the measured process variable, (iii)transmit a new controller output signal, or (iv) any combination orpermutation thereof The loop sample time may be at most about 1microsecond (μsec), 2 μsec, 3 μsec, 4 μsec, 5 μsec, 6 μsec, 7 μsec, 8μsec, 9 μsec, 10 μsec, 11 μsec, 12 μsec, 13 μsec, 14 μsec, 15 μsec, 20μsec, 25 μsec, 30 μsec, 40 μsec, 50 μsec, 60 μsec, 70 μsec, 80 μsec, 90μsec, 1 millisecond (msec), 5 msec, or 10 msec. The loop sample time maybe between any of the afore-mentioned sample times (e.g., from about 1μsec to about 90 μsec, from about 1 μsec to about 5 μsec, from about 5μsec to about 15 μsec, from about 15 μsec to about 30 μsec, from about30 μsec to about 90 μsec, from about 1 μsec to about 10 msec, or from 50μsec to 10 msec). The calculations may be performed at a time that is(e.g., substantially) equal to any of the afore-mentioned loop sampletimes. The calculations may be performed during the dwell time of the(e.g., transforming) energy beam, the intermission time of the (e.g.,transforming) energy beam, or any combination thereof The calculationmay be performed during the formation of one or more (e.g., successive)melt pools, between the formation of two (e.g., successive) melt pools(e.g., “between” may be inclusive or exclusive), or any combinationthereof. For example, the calculation may be performed during theformation of a single melt pool. The calculation may be performed duringa transformation of at least a portion of the material bed. Thecalculation may be performed between formation of two layers of hardenedmaterial, during formation of a layer of hardened material, duringformation of the 3D object, during the 3D printing process, or anycombination thereof The dwell time, intermission time, and/ortransforming energy beam (e.g., scanning energy beam and/or tilingenergy beam) may be any of the ones described in Patent Applicationserial number PCT/US16/66000, and in Provisional Patent Application Ser.No. 62/317,070, both of which are incorporated herein by reference intheir entirety. During the intermission time, the energy beam may have areduced power density that does not elevate the pre-transformed materialand/or target surface to at least a transformation temperature orhigher. For example, during the intermission, the energy beam may have apower density that allows the irradiated position at the target surfaceto heat up, but not transform. For example, during the intermission, theenergy beam may have a power density that negligibly heats up theirradiated position at the target surface. Negligibly is relative to the3D printing process. For example, during the intermission, the energybeam may be turned off

In some instances, the controller comprises a control loop bandwidth.The control loop bandwidth may be the frequency at which the closed loopresponse of the controlled variable is attenuated by about 3 dB from thesetpoint (e.g., the closed-loop magnitude response). The control loopbandwidth may be approximated as the point at which the open loop gainof the system is unity (also referred herein as the “crossover”frequency). The bandwidth of the closed-loop control system may be thefrequency range where the magnitude of the closed loop gain does notdrop below about −3 decibel (dB). The bandwidth of the control system,ω_(B), may be the frequency range in which the magnitude of theclosed-loop frequency response is greater than about −3 dB. Thefrequency ω_(B) may be the cutoff frequency. At frequencies greater thanω_(B), the closed-loop frequency response may be attenuated by more thanabout −3 dB. The frequency of the control loop bandwidth, ω_(B), may beat least about 0.1 Hertz (Hz), 0.2 Hz, 0.5 Hz, 0.7 Hz, 1 Hz, 1.5 Hz, 2Hz, 3 Hz, or 5 Hz. The frequency of the control loop bandwidth, ω_(B),may be between any of the afore-mentioned frequencies (e.g., from about0.1 Hz to about 5 Hz, from about 0.1 Hz, to about 1 Hz, from about 0.5Hz to about 1.5 Hz, or from about 1 Hz to about 5 Hz).

In some examples, the second PID controller reads an output of the first(e.g., outer loop) controller as a setpoint. The first PID controllermay control a more rapidly changing, or a less rapidly changingparameter (e.g., parameter characteristics) as compared to the parametercontrolled by the second PID controller. In some examples, the secondand the first PID controllers may control a parameter that changes insubstantially identical speed. In some embodiments, the workingfrequency of the cascade controller is increased as compared to using asingle PID controller. At times, the time constant may be reduced byusing cascaded PID controllers, as compared to using a single PIDcontroller. Instead of controlling the parameter (e.g., temperatureparameter, power parameter, and/or power density parameter) directly,the outer PID controller may set a parameter setpoint for the inner PIDcontroller. The inner PID controller may control the parameter directly.An error term of the inner controller may comprise a difference betweenthe parameter setpoint and the directly measured parametercharacteristics (e.g., temperature). The outer PID controller maycomprise a long time constant (e.g., may have a lengthy response time).The inner loop may respond at a shorter time-scale. The parametercharacteristics may comprise position, height, power, power density, ortemperature. The parameter characteristics may comprise a dwell time,pulse pattern, pulse frequency, footprint, acceleration, cross section,fluence, and/or velocity of the energy beam. The footprint may be afootprint of the energy beam on the target surface (e.g., exposed layerof the material bed).

In some embodiments, the controller continuously calculates an errorvalue during the control time. The error value may be the differencebetween a desired setpoint and a measured process variable. The controlmay be continuous control (e.g., during the 3D printing process, duringformation of the 3D object, and/or during formation of a layer ofhardened material). The control may be discontinuous. For example, thecontrol may cause the occurrence of a sequence of discrete events. Thecontrol may comprise a continuous, discrete, or batch control. Thedesired setpoint may comprise a temperature, power, power density, or ametrological (e.g., height) setpoint. The metrological setpoint mayrelate to the target surface (e.g., the exposed surface of the materialbed). The metrological setpoints may relate to one or more heightsetpoints of the target surface (e.g., the exposed (e.g., top) surfaceof the material bed). The temperature setpoint may relate to (e.g., maybe) the temperature of the material bed (e.g., at or adjacent to theexposed surface of the material bed). The temperature setpoint mayrelate to (e.g., may be) the temperature of or adjacent to a transformedmaterial (e.g., melt pool). The controller may attempt to minimize anerror (e.g., temperature and/or metrological error) over time byadjustment of a control variable. The control variable may comprise adirection and/or (electrical) power supplied to any component of the 3Dprinting apparatus and/or system. For example, direction and/or powersupplied to the: energy beam, scanner, motor translating the platform,optical system component, optical diffuser, or any combination thereof

In some embodiments, the setpoint (also herein “set point,” or“set-point”) is a desired or target value for an essential variable ofthe 3D printing system, method, algorithm, software and/or apparatus.The setpoint may be used to describe a standard configuration or normfor the system, method, algorithm, software, and/or apparatus. Departureof the variable from its setpoint may be a basis for an error-controlledregulation. The error controlled regulation may comprise a feed backand/or feed forward loop to alter (e.g., return) the system, method,algorithm, software and/or apparatus to its desired (e.g., normal)status (e.g., condition).

In some embodiments, the transforming energy beam irradiates at a firstpower P₁ (e.g., at its maximum power) on a position of the targetsurface (e.g., exposed surface of the material bed). A temperature ofthat (first) position can be sensed by a temperature sensor. Atemperature of that (first) position can be controlled by thecontroller. A temperature of a subsequently irradiated (second) positioncan be controlled by the controller (e.g., and influence the temperaturein the first position). When a target temperature of the positon isreached (e.g., as measured by the temperature sensor), the controllermay be used to hold that target temperature at a (e.g., substantially)constant value, for example, by reducing the power of the transformingenergy beam (e.g., to value P2, which is less than Pi). The power of theenergy beam may be measured as the power density of the energy beam. Insome embodiments, as a result of the temperature control by thecontroller, the power of the energy beam reaches a minimum power P_(min)(e.g., predetermined minimum power). At times, the power of thetransforming energy beam may reach a minimum power; at about that time:the power of the transforming energy beam may be (e.g., substantially)turned off, the power of the transforming energy beam may be (e.g.,substantially) reduced to a non-transforming power, the transformingenergy beam may relocate to another (e.g., distant) position, or anycombination thereof.

In some examples, the control is an active control. The control maycomprise controlling the FLS of the energy beam (e.g., footprint, orspot size). The control may comprise controlling the beam (e.g., energy)profile. The beam profile control may comprise using diffusive,microlens, refractive, or diffractive elements (e.g., optical elements).The beam profile control may comprise controlling the energy profile ofthe energy beam (e.g., flat top, Gaussian, or any combination thereof).The beam profile (e.g., FLS of the cross section and/or energy profile)may be altered during the 3D printing (e.g., during the formation of the3D object). During the formation of the 3D object may comprise duringformation of the layer of hardened material or a portion thereof.

In some examples, the transforming energy beam travels along the targetsurface in a trajectory (e.g., path). The transforming energy beam mayirradiate the target surface with a varied and/or constant powerdensity. The transforming energy beam may be generated by a power sourcehaving a varied and/or constant power. FIG. 32A shows an example ofenergy source power or a power density of the energy beam (collecrtivelydesignated as 3210), as a function of time; wherein thephysical-attribute profile pertains to the power of the energy source orthe power density of the energy beam respectively. For example, FIG. 32Ashows an example of an initial increase in power density (e.g., onturning the energy beam) at t₁, followed by a plateau during a periodfrom t₁ to t₂ (e.g., when irradiating at a constant power density),followed by a decrease during a period from t₂ to t₃ (e.g., whiledecreasing the power density as the transformed/transforming materialheats beyond a threshold temperature), followed by a second plateauduring a period from t₃ to t₄ (e.g., during an intermission when theenergy beam is turned off). For example, FIG. 32A shows an example of aninitial increase in the power of the energy source (e.g., on turning theenergy source to generate the energy beam) at t₁, followed by a plateauduring a period from t₁ to t₂ (e.g., when generating the energy beam ata constant power), followed by a decrease during a period from t₂ to t₃(e.g., while decreasing the power as the transformed/transformingmaterial heats beyond a threshold temperature), followed by a secondplateau during a period from t₃ to t₄ (e.g., during an intermission whenthe energy source is turned off). The transforming energy beam maytravel along the target (e.g., exposed) surface while having a (e.g.,substantially) constant or variable power density (i.e., power per unitarea). The variation may comprise initial increase in power density,followed by a decrease in the power density, or any combination thereof.The variation may comprise initial increase in power density, followedby a plateau, followed by a subsequent decrease in the power density, orany combination thereof The increase may be linear, logarithmic,exponential, polynomial, or any combination or permutation thereof Thedecrease and/or increase may be linear, logarithmic, exponential,polynomial, or any combination or permutation thereof. The plateau maycomprise of a (e.g., substantially) constant energy density. FIG. 32Bshows an example of energy source power, or a power density of theenergy beam (collecrtively designated as 3220) as a function of time;wherein the physical-attribute profile pertains to the power of theenergy source, or the power density of the energy beam respectively. Forexample, FIG. 32B shows a variation (e.g., oscillation) in the powerdensity of the energy beam, with three peak plateau power densities3221, 3222, and 3223, wherein each peak (plateau) is followed by adecrease (e.g., following the example in FIG. 32A) with three valleys(valley plateaus). For example, FIG. 32B shows a variation in the powerof the energy source, with three peak (plateau) power values 3221, 3222,and 3223, wherein each peak is followed by a decrease (e.g., followingthe example in FIG. 32A) with three valleys (valley plateaus). In theexample shown in FIG. 32B, all peak values correspond to the samemaximum physical-attribute (e.g., power) value, and all valley plateauscorrespond to the same minimum physical-attribute value, and the mannerof variation in the physical-attribute profile over time is the same(e.g., the manner and time of onset, peak plateau period, manner ofdecline, and valley plateau period, are the same). The manner of (e.g.,function used in) the variation in power density of the transformingenergy beam may be influenced by (i) a measurement (e.g., a signal ofthe one or more sensors), (ii) theoretically (e.g., by simulations),(iii) or any combination thereof. The duration and peak of the powerdensity plateau of the transforming energy beam may be influenced by (i)a measurement (e.g., a signal of the one or more sensors), (ii)theoretically (e.g., by simulations), (iii) or any combination thereof.The power density of the energy beam may fluctuate as a function of asensor measurement (e.g., of a temperature at the irradiated position orclose thereto) forming a sequence (e.g., of intermission times and dwelltimes). The fluctuated power density may comprise dwell times andintermission times. At least two of the intermission times in thesequence may be (e.g., substantially) of the same duration or ofdifferent duration. At least two of the intermission times in thesequence may be (e.g., substantially) of the same or different minimalpower density value. At least two of the dwell times in the sequence maybe (e.g., substantially) of the same duration or of different duration.At least two of the intermission times in the sequence may be (e.g.,substantially) of the same or different maximal power density value. Thepower of the energy source may fluctuate as a function of a sensormeasurement (e.g., of a temperature at the irradiated position or closethereto) forming a power sequence (e.g., of minimal power (e.g., off)times and maximal power times). At least two of the minimal power timesin the sequence may be (e.g., substantially) of the same duration or ofdifferent duration. At least two of the minimal power times in thesequence may be (e.g., substantially) of the same or different minimalpower density value. At least two of the maximal power times in thesequence may be (e.g., substantially) of the same duration or ofdifferent duration. At least two of the maximal power times in thesequence may be (e.g., substantially) of the same or different maximalpower density value. FIG. 32C shows an example of energy source power,or a power density of the energy beam (collecrtively designated as 3230)as a function of time; wherein the physical-attribute profile pertainsto the power of the energy source or the power density of the energybeam respectively. For example, FIG. 32C shows a variation (e.g.,fluctuation, oscillation, or pulse) in the power density of the energybeam, with three peaks (peak plateaus) 3231, 3232, and 3233, whereineach peak is followed by a decrease (e.g., following the example in FIG.32A) with three valleys (valley plateaus). For example, FIG. 32C shows avariation in the power of the energy source generating the energy beam,with three peak (plateau) power values 3231, 3232, and 3233, whereineach peak is followed by a decrease (e.g., following the example in FIG.32A) with three valleys (valley plateaus). In the example shown in FIG.33C, the peak values correspond to different maximum physical-attributevalues, the valley values correspond to different minimumphysical-attribute values, and the time-period of eachphysical-attribute pulse is the same (e.g., the time-period during peakplateau, valley plateau, and transition between them is respectively thesame among all the physical-attribute pulses). FIG. 32D shows an exampleof energy source power, or a power density of the energy beam(collecrtively designated as 3240) as a function of time; wherein thephysical-attribute profile pertains to the power of the energy source orthe power density of the energy beam respectively. For example, FIG. 32Dshows a variation (e.g., oscillation) in the power density of the energybeam, with three peak (plateau) power densities 3241, 3242, and 3243,wherein each peak is followed by a decrease (e.g., following the examplein FIG. 32A) with three valleys (valley plateaus). For example, FIG. 32Dshows a variation in the power of the energy source generating theenergy beam, with three peak (plateau) power values 3241, 3242, and3243, wherein each peak is followed by a decrease (e.g., following theexample in FIG. 32A) with three valleys (valley plateaus). In theexample shown in FIG. 33D, the peak values correspond to the samemaximum physical-attribute value (e.g., power density of the energybeam, or power of the energy source respectively), the valley valuescorrespond to the same minimum physical-attribute value, and the timeperiods of the physical-attribute pulses varies (e.g., the time-periodduring peak plateau, valley plateau, and transition between them variesamong the physical-attribute pulses). The physical-attribute pulses maycorrespond to forming melt pools. For example, each physical-attributepulse, may correspond to the formation of a melt pool. Thephysical-attribute pulses may correspond to froming tiles. For example,each physical-attribute pulse, may correspond to the formation of atile.

FIG. 1 shows an example of a 3D printing system 100 and apparatuses. Atransforming energy beam 101 is generated by an energy source 121. Thegenerated energy beam may travel through an optical mechanism 120 and/oran optical window 115 towards the material bed 104. The transformingenergy beam 101 may travel along a path to transform at least a portionof the material bed 104 into a transformed material. The transformedmaterial may harden into at least a portion of the 3D object. In theexample shown in FIG. 1, part 106 represents a layer of transformedmaterial within the material bed 104. The material bed may be disposedabove a platform. The platform may comprise a substrate 109 and/or abase 102. The platform may translate (e.g., vertically 112) using atranslating mechanism (e.g., an elevator 105). The translating mechanismmay travel in the direction to or away from the bottom of the enclosure111 (e.g., vertically). For example, the platform may decrease in heightbefore a new layer of pre-transformed material is dispensed by thematerial dispensing mechanism (e.g., 116). The top surface of thematerial bed 119 may be leveled using a leveling mechanism (e.g.,comprising parts 117 and 118). The mechanism (e.g., 3D printer 100) mayfurther include a cooling member (e.g., heat sink 113). The interior ofthe enclosure 126 may comprise an inert gas and/or an oxygen and/orhumidity reduced atmosphere. The atmosphere may be any atmospheredisclosed in patent application number PCT/US15/36802, titled“APPARATUSES, SYSTEMS AND METHODS FOR THREE-DIMENSIONAL PRINTING” thatwas filed on Jun. 19, 2015, which is incorporated herein by reference intheir entirety.

In one example of additive manufacturing, a layer of pre-transformedmaterial (e.g., powder material) is operatively coupled and/or disposedadjacent to the platform using the pre-transformed material dispensingmechanism (e.g., 116); the layer is leveled using a leveling mechanism(e.g., 117 and 118 collectively); an energy beam 101 is directed towardsthe material bed to transform at least a portion of the material bed toform a transformed material; the platform is lowered; a new layer ofpre-transformed material is disposed into the material bed; and that newlayer is leveled and subsequently irradiated. The process may berepeated sequentially until the desired 3D object is formed from asuccessive generation of layers of transformed material (e.g., relatingto a virtual model of a requested 3D object). In some examples, as thelayers of transformed material harden, they may deform upon hardening(e.g., upon cooling). The methods, systems, apparatuses, and/or softwaredisclosed herein may control at least one characteristic of the layer ofhardened material (or a portion thereof), such as their planarity,resolution, and/or deformation. For example, the methods, systems,apparatuses, and/or software disclosed herein may control the degree ofdeformation. The control may be an in situ control. The control may becontrol during formation of the at least a portion of the 3D object. Thecontrol may comprise closed loop control. The portion may be a surface,layer, multiplicity of layers, portion of a layer, and/or portion of amultiplicity of layers. The layer of hardened material within the 3Dobject may comprise a multiplicity of melt pools. The layers'characteristics may comprise planarity, curvature, or radius ofcurvature of the layer (or a portion thereof). The characteristics maycomprise the thickness of the layer (or a portion thereof). Thecharacteristics may comprise the smoothness (e.g., planarity) of thelayer (or a portion thereof).

The methods, systems, apparatuses, and/or software described herein maycomprise providing a first layer of pre-transformed material (e.g.,powder) in an enclosure to form a material bed (e.g., powder bed). Thefirst layer may be provided on a substrate or a base. The first layermay be provided on a previously formed material bed (e.g., layer ofpre-transformed material). At least a portion of the first layer ofpre-transformed material may be transformed by using an energy beam. Forexample, an energy beam may irradiate the at least a portion of thefirst layer of pre-transformed material to form a first transformedmaterial. The first transformed material may comprise a fused material.The methods, systems, apparatuses, and/or software may further comprisedisposing a second layer of pre-transformed material adjacent to (e.g.,above) the first layer. At least a portion of the second layer may betransformed (e.g., with the aid of the energy beam) to form a secondtransformed material. The second transformed material may at least inpart connect to the first transformed material to form a multi-layeredobject (e.g., a 3D object). Connect may comprise fuse, weld, bond,and/or attach. The first and/or second layer of transformed material maycomprise a first and/or second layer of hardened material respectively.The first and/or second layer of transformed material may harden into afirst and/or second layer of hardened material respectively.

The methods, systems, apparatuses, and/or software may comprisecontrolling at least a portion of the deformation of at least the firstor second layers of hardened material. The methods, systems,apparatuses, and/or software may comprise controlling at least a portionof the deformation of at least a portion of the first and/or secondlayers of hardened material. The methods, systems, apparatuses, and/orsoftware may comprise controlling the deformation of at least the firstor second layers of hardened material. The methods, systems,apparatuses, and/or software may comprise controlling the deformation ofthe multi-layered material. The deformation may comprise a curvature (orplanarity).

In some embodiments, the deformation may be measured and/or controlled(e.g., regulated) during the formation of the 3D object (e.g., formationof a portion of a layer of the 3D object). In some embodiments, thecurvature (or planarity) may be measured and/or controlled during theformation of the 3D object. In some embodiments, the deformation may bemeasured and/or controlled during the transformation operation. In someembodiments, the curvature (or planarity) may be measured and/orcontrolled during the transformation operation (e.g., in real-time). Insome embodiments, the curvature (or planarity) may be measured and/orcontrolled during transforming one portion of a first layer and/ortransforming a second portion of a second layer. The first and secondlayers can be different layers.

In some embodiments, at least one characteristic of the energy beamand/or source is controlled (e.g., regulated) and/or monitored. Thecontrol may be during the formation of the 3D object. For example, thecontrol may be during the transformation operation (e.g., transformingat least a portion of the layer of pre-transformed material). Thecontrol may comprise controlling the deformation. The control maycomprise controlling the planarity (e.g., of at least a portion of alayer). The control may comprise controlling the curvature (e.g., of atleast a portion of a layer). The control may comprise controlling thedegree and/or direction of deformation (e.g., of at least a portion of alayer). The control may result in reduced deformation as compared to anon-controlled process. For example, the control may result in reducedcurvature as compared to a non-controlled process. The control mayresult in an increased radius of curvature as compared to anon-controlled process. The control may result (e.g., substantially) nodeformation as compared to a non-controlled process which results in adeformation. The control may result in (e.g., substantial) lack ofcurvature as compared to a non-controlled process which results incurvature. The control may result in at least a portion of the layerbeing planar (e.g., flat), as compared to a non-controlled processgenerating the at least a portion of the layer as non-planar. Thecontrol may result in a (e.g., substantially) smooth surface as comparedto a non-controlled process (generating a respective surface that issubstantially rough).

The control may include controlling (e.g., regulating) the energy,energy flux, dwell time, pulse pattern, pulse frequency, footprint,acceleration, and/or velocity of the energy beam. The control mayinclude controlling (e.g., regulating) the power of the energy source.The footprint may be a footprint of the energy beam on the targetsurface (e.g., exposed layer of the material bed). The accelerationand/or velocity may be the acceleration and/or velocity (respectively)in which the energy travels (e.g., laterally) along the target surface(e.g., exposed surface of the material bed). The energy beam may travelalong a path. The energy beam may be a pulsing energy beam. The controlmay include controlling the pattern of the pulses, dwell time withineach pulse, and/or the delay length (e.g., intermission time, or beamoff time) between pulses.

In some embodiments, an energy profile of the (e.g., transforming)energy beam may be controlled (e.g., in real time and/or in situ). Insome embodiments, a measured (e.g., detectable) energy profile may becontrolled (e.g., in real time and/or in situ). In some embodiments, ameasured physical-attribute profile may be controlled (e.g., in realtime and/or in situ). The physical-attribute may be artificially induced(e.g., using an energy source). The physical-attribute profile may be ameasurement signal profile. The physical-attribute profile may comprise(i) temperature, (ii) FLS of an energy beam footprint (on the targetsurface), (iii) metrology (of the target surface), (iv) power of theenergy source generating the transforming energy beam, (v) energydensity of the transforming energy beam, (vi) radiation from the targetsurface (e.g., at or adjacent to the footprint) or (vii) lightreflection. The light reflection may comprise scattered light reflectionor specular light reflection. The irradiation may be heat irradiation(e.g., IR irradiation). The physical-attribute may be of (e.g.,correspond to), for example, a melt pool, or transformed portion of thematerial bed. The control may be any control disclosed herein. Forexampel, the control may comprise a closed loop control. The control maycomprise a feedback control. The control may be during the 3D printing(e.g., in real time). The energy beam may comprise a pulsing energy beamcomprising one or more pulses (e.g., two or more pulses). The pulse maybe a pulse in terms of (e.g., in correlation with and/or affecting) thephysical-attribute (e.g., detectable energy). The pulse in therms of(e.g., pertaining to) the physical-attribute (termed also herein as“physical-attribute pulse”) may comprise one or more pulses of the(e.g., transforming) energy beam. For example, a physical-attributepulse may be a result of a single energy beam pulse, or of a pluralityof pulses of the energy beam. The physical-attribute pulse may beeffectuated by pulse-width modulation (abbreviated as “PWM”) of theenergy beam. The physical-attribute pulses may correspond to formationof melt pools, wherein each physical-attribute pulse corresponds toformation of a melt pool. FIG. 22B shows an example of a pulsing(measured) physical-attribute profile over time. In the example shown inFIG. 22B, the physical-attribute may be temperature 2220. FIG. 32B showsan example of a pulsing physical-attribute profile over time. In theexample shown in FIG. 32B, the physical-attribute may be a power of theenergy source generating the energy beam, or a power density of theenergy beam. The measured physical-attribute profile may be controlledwithin the physical-attribute pulse (e.g., over the physical-attributepulse time-period). The energy profile of the energy beam may becontrolled within the physical-attribute pulse in real-time (e.g., insitu) during the 3D printing process. In some embodiments, one or moreindividual pulses may be controlled during their pulsing time (e.g., inreal time). For example, the shape of physical-attribute pulse or any ofits portions may be controlled. The portions may be controlledindividually (e.g., in real-time). The physical-attribute pulse portionsmay comprise a leading edge, plateau (if any), trailing edge, dwelltime, intermission, or any combination thereof. In some embodiments, thephysical-attribute pulse does not include all of the followingcomponents: a leading edge, plateau (if any), trailing edge, dwell time,and intermission. FIG. 22A shows an example of a measuredphysical-attribute pulse (e.g., temperature 2200 variation) profile as afunction of time, having a dwell time from t₁ to t₄ and an intermissiontime from t₄ to t₅. The dwell time in example shown in FIG. 22A isdivided into a leading edge 2211, a plateau 2212, and a tailing edge2213. The intermission in the example shown in FIG. 22A is 2214. Thephysical-attribute profile (e.g., temperature profile) over time may bealong a trajectory of the transforming energy beam on the targetsurface. The physical-attribute profile may be derived from sensormeasurements. The sensor may be any sensor or detector described herein(e.g., a temperature sensor). The temperature sensor may sense aradiation (or a radiation range) that is emitted from an area at thetarget surface that coincides with the transforming energy beamfootprint, or adjacent threto (e.g., within a radius equal to at mostabout 2, 3, 4, 5, or 6 footprint diameters measured from the center ofthe footprint). The radiation may be IR radiation. The intensity and/orwavelength of a radiation emitted from an area may correlate to thetemperature at that area. The

The control may rely on at least one measurement of at least onephysical-attribute (e.g., aspect, circumstance, event, experience,incident, reality, fact, incident, situation, circumstance, or anycombination thereof). The physical-attribute may be susceptible to theamount and/or density of energy emitted by the energy beam. Thephysical-attribute may vary depending on the amount and/or density ofenergy emitted by the energy beam. In some embodiments, at least onephysical-attribute type may be controlled (e.g., regulated, monitored,modulated, varied, altered, restrained, managed, checked, and/or guided)in real-time during the physical-attribute pulse. Real time may beduring the formation of the 3D object, during the formation of the layerof hardened material, during formation of a wire (e.g., forming at leasta portion of a layer of hardened material), during formation of a hatchline (e.g., while forming at least a portion of a layer of hardenedmaterial), during formation of a melt pool, during thephysical-attribute pulse, or any combination thereof

In some embodiments, the physical-attribute controlled during thephysical-attribute pulse (e.g., in real time during the 3D printingprocess) comprises a temperature, FLS (e.g., of a melt pool), crystalphase, solid morphologies (e.g., metallurgical phase), stress, strain,defect, surface roughness, light scattering (e.g., from a surface),specular reflection (e.g., from a surface), change in polarization ofreflected light (e.g., from a surface), surface morphology, or surfacetopography. The surface can be the target surface. Thephysical-attribute may correspond to at least one melt pool. The surfacecan be the exposed surface of the material bed, 3D object, melt pool,portion of transformed material, or any combination thereof The defectmay comprise cracking or deformation. The deformation may comprisebending, buckling, and/or warping. The physical-attribute (e.g.,detectable energy) may arise at the material bed, melt pool, area justadjacent to the melt pool, target surface (e.g., exposed surface of thematerial bed), or any combination thereof. For example, the temperature(physical-attribute) may comprise temperature of the material bed, meltpool, area (e.g., just) adjacent to the melt pool, exposed surface ofthe material bed, or any combination thereof. Adjacent may be within adistance that is substantially equal to or equal to at most about 5%,10%, 20%, 30%, 40% or 50% of the FLS of the melt pool. Adjacent may bewithin any distance between the afore-mentioned percentages of the meltpool FLS (e.g., from about 5% to about 50%, from about 5% to about 30%,or from about 5% to about 10% of the respective FLS of the melt pool).The FLS physical-attribute may comprise a FLS of the melt pool, hatchline, hatch spacing, layer of pre-transformed material (e.g., powdermaterial), or any combination thereof For example, the FLS of the meltpool may comprise the diameter or depth of the melt pool. In someembodiments, the heating profile and/or the cooling profile (e.g., ofthe material bed, melt pool, area just adjacent to the melt pool,exposed surface of the material bed, or any combination thereof) may becontrolled during the physical-attribute pulse as a result of the amountof energy radiated into the material bed during different time-portionswithin the physical-attribute pulse. In some embodiments, the expansionand/or contraction profile (e.g., of the melt pool, of the hatch line,of the hatch spacing, or of the layer of pre-transformed material (e.g.,powder material), or any combination thereof) may be controlled duringdifferent time-portions within the physical-attribute pulse. The shapeof the physical-attribute pulse may be controlled (e.g., in real timeand/or in situ during the 3D printing process). The physical-attributepulse may comprise a dwell time and an intermission. The dwell time maycomprise a time interval. In some examples, at least one-time intervalof the physical-attribute pulse may be controlled. The time interval maybe a portion of the physical-attribute pulse dwell time (e.g., from t₁to t₂ in FIG. 22A), or the entire physical-attribute pulse dwell time(e.g., from t₁ to t₅ in FIG. 22A).

The control may comprise forming at least two physical-attribute pulses(e.g., all the physical-attribute pulses) that are substantiallyidentical (e.g., completely identical, or almost identical) in terms ofthe measured physical-attribute profile (as a function of time). FIG.22B shows an example of three physical-attribute pulses (2221, 2222, and2223, wherein the physical-attribute correlates to temperature as afunction of time) that are identical with respect to the measured energy(as a function of time). The control may comprise forming at least twophysical-attribute pulses that are different from one another withrespect to the physical-attribute profile (as a function of time), in acontrolled manner (e.g., by keeping the temperature physical-attributeand/or FLS physical-attribute controlled). Different may be with respectto the physical-attribute amplitude, its duration, or any combinationthereof (e.g., within the pulse). Different may be with respect to wayin which the physical-attribute reaches its maximum, way it reaches itsminimum, or any combination thereof (e.g., within the pulse). Differentmay be with respect to peak maximum, and/or peak minimum of the aphysical-attribute (e.g., a measured energy). FIG. 22C shows an exampleof measured temperature 2230 over time of three pulses (2231, 2232, and2233) that are different with respect to the physical-attributeamplitude and (e.g., substantially) identical with respect totime-period of the pulse. FIG. 22D shows an example of measuredtemperature 2240 over time of three physical-attribute pulses (2241,2242, and 2243) that are different in their pulse duration of thephysical-attribute pulse and (e.g., substantially) identical withrespect to their maximum and minimum peak intensities (e.g., minimum andmaximum temperatures). FIG. 22C shows an example of two pulses (2231,and 2232) that are different in their minimum peak intensity position(e.g., minimum temperature).

The control may comprise forming at least two physical-attribute pulses(e.g., all the physical-attribute pulses) that are (e.g., substantially)identical in terms of temperature profile as a function of time. Thecontrol may comprise forming at least two pheonomenon pulses that aredifferent in terms of temperature profile versus time in a controlledmanner (e.g., by keeping the energy profile of the energy beam and/orthe FLS physical-attribute controlled). The FLS physical-attribute maycomprise a FLS of the melt pool, hatch line, hatch spacing, layer ofpre-transformed material (e.g., powder material), or any combinationthereof The control may comprise forming at least two physical-attributepulses (e.g., all the pulses) that are identical in terms of FLS profile(e.g., of a melt pool) versus (e.g., as a function of) time. The controlmay comprise forming at least two physical-attribute pulses (e.g., allthe pulses) that are different in terms of temperature profile versus(e.g., as a function of) time in a controlled manner (e.g., by keepingthe energy profile of the energy beam and/or the temperaturephysical-attribute controlled). The temperature physical-attribute maycomprise temperature of the material bed, melt pool, area just adjacentto the melt pool, exposed surface of the material bed (e.g., position(s)therein), or any combination thereof. The physical-attribute maycomprise a physical-attribute, occurance, or event.

The physical-attribute profile may comprise a temperature profile of amelt pool. A physical-attribute pulse may be a temperature pulse of theexposed surface of the material bed (e.g., an area therein). Forexample, at time t₁ (e.g., in FIG. 22A), the temperature of a positionin the powder bed in which a melt pool is to be formed, begins to raise,and reaches a maximum level at t₂ (e.g., in FIG. 22A); the temperatureof the melt pool is then held in (e.g., substantially) the same maximumlevel until time t₃ (e.g., in FIG. 22A); after which it begins todecline (e.g., as the melt pool cools down) until it reaches a certainminimum level at t₄ (e.g., in FIG. 22A). The temperature of the exposedsurface of the material bed may be held in an (e.g., substantially)identical temperature until time t₅ (e.g., in FIG. 22A), in which a newmelt pool is being formed and a new physical-attribute pulse isgenerated. The designation t₁₋₅ can refer to those in FIG. 22A.

In some embodimetns, the physical-attribute profile comprises a powerpulse profile of an energy source that generates the energy beam. Forexample, at time t₁ (e.g., in FIG. 32A), the power of the energy sourcemay be turned on to reach a maximum power threshold value; the power maybe held at that maximum power value until a different physical-attributethat is affected by the energy beam (e.g., corresponding to thetemperature at the irradiated position) reaches a desired thresholdvalue of that different physical-attribute (e.g., corresponding to thetemperature), at time t₂ (e.g., in FIG. 32A); in order to (e.g.,substantially) keep that different physical-attribute at its desiredthreshold value, the power of the energy source may be reduced until itreaches a minimum level is reached at t₄ (e.g., in FIG. 32A). The powermay be held at that minimum value, or entirely turn off until time t₅(e.g., in FIG. 32A), in which a new power pulse may be generated. Thetimes t₁-t₅ in FIG. 22A may be the same as the times t₁-t₅ in FIG. 32A.

In some embodiments, the physical-attribute profile comprises a powerdensity pulse profile of an energy beam that generates a transformedmaterial. For example, at time t₁ (e.g., in FIG. 32A), the power densityof the energy beam may be turned on to reach a maximum power densitythreshold value; the power density may be held at that maximum valueuntil a different physical-attribute that is affected by the energy beamradiation (e.g., temperature at the irradiated position) reaches adesired threshold at time t₂ (e.g., in FIG. 32A); in order to (e.g.,substantially) keep that different physical-attribute at a desiredthreshold value of that different physical-attribute, the power densityof the energy beam may be reduced until it reaches a minimum level isreached at t₄ (e.g., in FIG. 32A). The power density may be held at thatminimum value, or entirely turn off until time t₅ (e.g., in FIG. 32A),in which a new power density pulse may be generated. The times t₁-t₅FIG. 22A may be the same as the times t₁-t₅ in FIG. 32A.

The physical-attribute profile may comprise a diameter profile of a meltpool. The physical attribute may be an artificially induced phenomenon.A physical-attribute pulse may be a diameter pulse of a melt pool. Forexample, at time t₁ (e.g., in FIG. 22A), an area at a position of atarget surface (e.g., an exposed surface of a material bed) begins totransform into a melt pool; the diameter of the melt pool may begins toexpand, and reaches a maximum level at t₂ (e.g., in FIG. 22A, wherein2200 represents the diameter of the melt pool); the diameter of the meltpool is then held in (e.g., substantially) the same maximum diameteruntil time t₃ (e.g., in FIG. 22A); after which it begins to shrink(e.g., as the melt pool cools down) until it reaches a certain minimumlevel at t₄ (e.g., in FIG. 22A). The diameter of the melt pool may beheld in an (e.g., substantially) identical temperature until time t₅(e.g., in FIG. 22A), in which a new melt pool is being formed and a newphysical-attribute pulse is generated. By controlling the shape of oneor more portions of the physical-attribute pulse (e.g., by controllingthe temperature at the target surface, at least one characteristic ofthe energy beam, and/or at least one characteristic of the energy sourcesuch as its power), the size of the melt pool can be controlled. Forexample, the size of a plurality of melt pools can be controlled (e.g.,to be (e.g., substantially) identical, see FIG. 35). The designationt₁₋₅ can refer to those in FIG. 22A. The control may comprise directly(e.g., gradually) adjusting the power of the energy beam. Additionallyor alternatively, the control may comprise modulating the energy beam byusing pulse width modulation (PWM). The control may comprise generating(e.g., irradiating) pulses of the energy beam that are short relative tothe duration of the physical-attribute pulse. The control may alter oneor more functions of the 3D printing. For example, the control may varythe size of transformed area. The size may be the volume and/or the FLS.The transformed area may be on the surface of at least a portion of thelayer as part of the 3D object. The transformed area may be atransformed area in the material bed. The transformed area may be atransformed area in the target surface. The transformed area maycomprise a melt pool. The transformed area may be the melt pool. Thetransformed area may include an adjacent area to the afore-mentionedareas (e.g., within at least about 2, 3, 4, 5, 6, 7, or 8 melt pooldiameters). The control may take into account at least one temperaturemeasurement at the irradiation position and/or adjacent thereto. Theirradiation position may be a position in which the energy beaminteracts with the target surface (e.g., to transfer a portion of itinto a transformed material). Adjacent may be within at least about 0.1micrometer (μm), 0.5 μm, 1 μm, 1.5 μm, 2 μm, 3 μm, 4 μm, 5 μm, 6 μm, 7μm, 8 μm, 9 μm, or 10 μm from the irradiation position (e.g., center orrim of the irradiation position). Adjacent may be within at most about50 μm, 10 μm, 9 μm, 8 μm, 7 μm, 6 μm, 5 μm, 4.5 μm, 4 μm, 3.5 μm, 3 μm,2.5 μm, 2 μm, 1.5 μm, 0.75 μm, 0.5 μm, 0.4 μm, 0.3 μm, 0.2 μm, or 0.1 μmfrom the irradiation position. Adjacent may be of any value between theafore-mentioned values (e.g., from about 0.1 μm to about 1 μm, fromabout 1 μm to about 10 μm, or from about 0.1 μm to about 50 μm). Thesevalues may correspond to “adjacent to the irradiation position”, or to“adjacent to the transformed area.”

In an aspect, the one or more sensors sense one or more positions of thetarget (e.g., exposed) surface. The exposed surface may be of thematerial bed, of the transformed material, of the 3D object, or anycombination thereof The exposed surface of the material bed may comprisea layer of material disposed prior to the formation of the 3D object.The exposed surface of the material bed may comprise a layer of materialthat was used to form the last (e.g., previously) formed hardened layerof the 3D object. The exposed surface of the material bed may comprise alayer of material that was disposed subsequent to the formation of thelast formed hardened layer of the 3D object. FIG. 14 shows an example ofa material bed 1410 having an exposed surface 1412; and the exposedsurface 1412 is disposed before formation of the last hardened layer of3D object 1400. The exposed surface of the material bed may comprise anewly dispensed layer of pre-transformed material in the material bed.In some instances, the 3D object may protrude from the newly dispensedlayer of pre-transformed material. In some instances, the 3D object maybe completely covered by the newly dispensed layer of pre-transformedmaterial. FIG. 15 shows an example of a material bed 1510, with anexposed surface 1514; the surface 1512 is of a previously dispensedlayer of pre-transformed material; and the exposed surface 1514 is of anewly dispensed layer of pre-transformed material (e.g., subsequent tothe formation of the last layer of hardened material of the 3D object1500). In the example of FIG. 15, the 3D object protrudes the newlydispensed layer of pre-transformed (e.g., powder) material. The datafrom the one or more sensors may be used (e.g., by the controller and/ora processing unit) to provide a map of at least a portion of the targetsurface. The map may be generated during the process of printing (e.g.,forming) the 3D object. The processing unit may be a part of thecontroller. The processing unit may be separate from the controller. Themap may be generated during the 3D printing process. The map may bealtered during the 3D printing process (e.g., based on sensor input).The map may be generated and/or altered during the 3D printing process.The map may be generated with a relatively high frequency and/orresolution. For example, the frequency may substantially equal any ofthe frequencies recited herein for the sensor measurement frequency. Theresolution may be any resolution mentioned herein. For example, theresolution of the sensor may be from about 10% to about 190% of theaverage or mean FLS of the particulate material in the material bed.

In some embodiments, the one or more sensors sense one or more positionsof at least a portion of the 3D object. The one or more sensors maysense one or more positions of at least a portion of the 3D object thatprotrudes from the exposed surface of the material bed. FIG. 14 shows anexample of a 3D object 1400 that protrudes from the exposed surface 1412of the material bed 1410 that is operatively coupled and/or disposedadjacent to a platform 1411. In the example of FIG. 14, the 3D objectprotrudes by a height 1413 from the exposed surfaced 1412 of thematerial bed 1410. The one or more sensors may measure the one or morepositions of the exposed surface using a contact method, non-contactmethod, or any combination thereof. The one or more positions of theexposed surface may comprise vertical, horizontal, and/or angularpositons. The angular positon may include compound or planar angle. Themeasurement may comprise the height (e.g., thickness) of thepre-transformed material disposed above a layer of hardened material.The sensors may sense an energy beam. The positions sensed by the one ormore sensors may be effectuated by sensing an energy beam. The energybeam may comprise the transforming energy beam or the sensing energybeam. The energy beam may be reflected from the target (e.g., exposed)surface. The reflected energy beam may be sensed by the one or moresensors. FIG. 4 shows an example of an energy beam 420 that is reflectedfrom the target surface 408 and is sensed by the sensor receiver part418. The exposed surface may comprise the exposed surface of thematerial bed, or of the at least a portion of the 3D object. The exposedsurface may be of a transformed portion of the material bed that is nota portion of the 3D object (e.g., debris, flag, or auxiliary support).The exposed surface may comprise an exposed surface of the material bedthat has altered its position due to the formation of at least a portionof the 3D object, which portion is covered by pre-transformed materialas part of (e.g., within) the material bed. For example, the exposedsurface may comprise an exposed surface of the powder bed that hasaltered its position due to the formation of at least a portion of the3D object, which 3D object is covered by powder material within thepowder bed. FIG. 16 shows an example of a 3D object 1600 that is coveredby a material bed 1610, which formation of the 3D object caused aportion of the exposed surface of the material bed to alter in thedirection of the arrow 1613.

At times, a new layer of hardened material is deposited on a portion ofa 3D object. The portion of the 3D object may include one or more layers(e.g., of hardened material). The portion of the 3D object maysubstantially adhere to (e.g., not substantially deviate from) a modelof the desired 3D object. The one or more layers within the portion ofthe 3D object may substantially adhere to (e.g., not substantiallydeviate from) a model of the desired 3D object. The one or more layersof the 3D object may be substantially non-deformed. Substantially may berelative to the intended purpose of the 3D object.

In certain instances, the portion of the 3D object deviates from themodel of the desired 3D object. The deviation may comprise a correctivedeviation. The deviation may comprise a corrective deformation. Theportion of the 3D object may deviate from a model of the desired 3Dobject. The one or more layers within the portion of the 3D object maydeviate from a model of the desired 3D object. The one or more layers ofthe 3D object may be substantially deformed as compared to therespective one or more slices in the model of the desired 3D object. Themanner of forming (e.g., printing) the one or more layers may deviatefrom a model of the desired 3D object. The path in which thetransforming energy beam progresses, may deviate from a slice of themodel of the desired 3D object. The model of the desired 3D object maybe a desired model. In some examples, a deviated model may be used toprovide (3D printing) instructions for the transformation of at least aportion of the material bed (e.g., to form the 3D object). In someexamples, a deviated model may be used to provide instructions for theenergy beam path. The deviated model may allow the transformed materialto take a shape that (e.g., substantially) corresponds to the desired 3Dobject (e.g., upon hardening, e.g., upon solidifying). At least aportion of the desired model (e.g., slice thereof) may undergo adeviation conversion to form the deviated model The deviation may be acorrective deviation. The deviation may be substantial (e.g.,measurable). The deviation may be controlled (e.g., by at least onefunction used in the 3D printing). The deviation of the portion oftransformed material that is materialized during the printing (e.g.,material transformation) operation, may substantially correspond to thedeviation that is recommended by the deviated model. The (virtual) modelof the requested 3D object that underwent the deviation may be referredherein as the “deviated model.” A desired deviation of the portion(e.g., layer) may be effectuated when a portion of transformed material(e.g., layer), which was generated according to the deviated model(e.g., slice thereof), hardens (e.g., cools). The desired deviation ofthe portion of transformed material may be referred to herein as a“target deviation.” The target deviation may be measured, anticipated bymodeling (e.g., thermo-mechanical modeling), anticipated according tohistorical data, or any combination or permutation thereof The targetdeviation may be reached generating the transformed material. The targetdeviation may be reached upon hardening (and/or cooling) the portion oftransformed material. The deviation of the portion of transformedmaterial may be controlled (e.g., in spatial orientation and/ormagnitude). The controlling operation may comprise controlling theportion of transformed material such that it will (e.g., substantially)correspond to the target deformation (e.g., upon hardening and/orcooling). FIG. 6 shows examples of a 3D object before and afterhardening (by cooling). 3D Object 601 represents an intermediate 3Dobject that has not completely hardened, whereas 3D object 602represents the object 601 that has completely hardened. In someembodiments, object 603 may represent an example of a vertical crosssection in a virtual model of a requested 3D object depicting the slices(e.g., layer instructions for printing the 3D object). In someembodiments, 603 may represent an example of a cross section of a 3Dobject that was printed but did not completely harden. Object 604represents an example of a cross section in a completely hardened 3Dobject (e.g., final 3D object). Object 604 represents an example of avertical cross section in the printed 3D object that substantiallycorresponds (e.g. match) the desired 3D object, with the lines depictinglayer boundaries. Slice 605 was printed as a layer that deviates fromthe desired 3D object model, which printing was according toinstructions from the deviated model. Upon complete hardening, the layerassumed a shape (e.g., 606) that allowed the printed 3D object tosubstantially correspond to the desired 3D object. The assumed shape may(e.g., substantially) correspond to a modeling of the hardening of thetransformed material (e.g., transformed material layer). The targetdeformation may be determined using historical data and/or modeling(e.g., of the hardening and/or cooling). The assumed shape may (e.g.,substantially) correspond to the target deformation (e.g., targetshape). The manner of assuming the final shape of the at least one layermay be controlled. The control may be any of the control methoddisclosed herein. The control may be control of at least one functioninvolved in 3D printing. For example, the control may be control of atleast one characteristic of the energy beam. For example, the controlmay be control of a temperature of the hardened material and/or materialbed (e.g., during the 3D printing).

The methods, software, and systems described herein may comprisecorrective deformation of a 3D model of the desired 3D structure, thatsubstantially result in the requested 3D structure. The correctivedeformation may take into account features comprising (i) stress withinthe forming structure, (ii) deformation of material as it hardens toform at least a portion of the 3D object, (iii) the manner oftemperature depletion during the 3D printing process, or (iv) the mannerof deformation of the transformed material as a function of the densityof the material within the material bed (e.g., powder material within apowder bed). The modification may comprise alteration of a path of alayer (or portion thereof) in the 3D model. The alteration of the pathmay comprise alteration of the path filling at least a portion of thelayer (e.g., cross section of the 3D object), e.g., which path maycomprise hatching. The alteration of the path (e.g., hatching) maycomprise alteration of the direction of path (e.g., hatching), thedensity of the path (e.g., hatch) lines, the length of the path (e.g.,hatch) lines, or the shape of the path (e.g., hatch) lines. Themodification may comprise alteration of the thickness of the 3D object(or a portion thereof, e.g., layer), for example, during its transformedstate (e.g., before complete hardening). The modification may comprisevarying at least a portion of a cross section (e.g., slice) of the 3Dmodel by an angle (e.g., planer or compound angle), or inflicting to atleast a portion of a cross section a radius of curvature (i.e., bendingat least a portion of the cross section of a 3D model). Correctivedeformation may be any corrective deformation disclosed in patentapplication Ser. No. 62/239,805, and PCT application numberPCT/US16/34857, both of which are incorporated herein by reference intheir entirety. The corrective deviation from the intended 3D structuremay be termed herein as “geometric correction.” FIG. 17 shows examplesof various stages in formation of a 3D object 1703 represented as threelayers (e.g., numbered 1-3 in object 1703), which is shown as a verticalcross section and is situated on a platform 1704. The first formed layeris formed as a negatively curved layer #1 of object 1701. Once thesecond layer (#2 of object 1702) is formed, the first layer #1 mayflatten out (e.g., its radius of curvature is increased, its curvatureis reduced (e.g., approaches zero)). Once the third layer (#3 of object1703) is formed, the layers of the 3D object become substantially flat(e.g., planar). Layer #1 may be said to be formed as a correctivelydeformed layer. The corrective deformation may enable a formation of a(e.g., substantially) non-deformed 3D object. The manner of printing oneor more subsequent layers to the correctively deformed layers may takeinto account the (e.g., in situ and/or real time) measurements from theone or more sensors. The corrective deformation may be of an entirelayer of hardened material, or a portion thereof The correctivedeformation may be of at least a portion of the layer of hardenedmaterial as part of a 3D object.

In some embodiments, the sensor comprises an imaging device. The imagingdevice may comprise multi-spectral imaging, single spectral imaging, ornon-spectral imaging. The non-spectral imaging may comprise acoustic,electro, or magnetic imaging (e.g., electromagnetic imaging). Themulti-spectral imaging may comprise detecting red body radiation (e.g.,emitted from the target surface). The imaging device may comprise acamera. The imaging device may image a target surface (e.g., exposedsurface of the material bed, 3D object, or melt pool). The imagingdevice may image the temperature and/or metrology (e.g.,dimensionality). The imaging device may image a melt-pool temperature,shape and/or FLS (e.g., diameter, or depth). The imaging device mayimage a vicinity of melt-pool temperature, shape and/or FLS (e.g.,diameter, or depth). The imaging device may image a zone affected by themelt pool (e.g., heat thereof). The zone affected by the heat of themelt pool is termed herein “heat affected zone” (e.g., FIG. 26A, 2610).The imaging device may image the generation and/or hardening of at leasta portion of the melt pool.

In some embodiments, the non-contact measurement includes at least oneoptical measurement. The optical measurement (e.g., by the opticalsensor) may comprise measurement by an image sensor (e.g., CCD camera),optical fiber (e.g, optical fiber bundle), laser scanner, orinterferometer. The interferometer may comprise a white light or apartial coherence interferometer.

In some embodiments, the optical measurement and/or the analysis thereofcomprise (e.g., superimposed) waves (e.g., electromagnetic waves). Thesuperimposed waves may be used to extract information about areflection(s) of these waves from the target surface. The informationmay comprise relative location, location alteration (e.g.,displacement), refractive index alteration, or surface changes (e.g.,irregularities). The optical measurement of the reflection(s) and/or theanalysis thereof may comprise using Fourier transform spectroscopy(e.g., of continuous waves). The optical measurement of thereflection(s) and/or the analysis thereof may comprise combining two ormore waves (e.g., super positioning waves). The optical sensor maycomprise a mirror or a beam splitter. The mirror may be substantiallyfully reflective, or partially reflective (e.g., a half-silveredmirror). The mirror may be (e.g., controllable) translating (e.g.,horizontally, vertically, and/or rotationally, e.g., along an axis). Thepartially reflective mirror may be a beam splitter. The interferometermay comprise homodyne or heterodyne detection. The interferometer maycomprise a double path or common path interferometer. The interferometermay comprise wave front splitting or amplitude splitting. Theinterferometer may comprise a Michelson, Twyman-Green, Mach-Zehnder,Sagnac (e.g., zero-area Sagnac), point diffraction, lateral shearing,Fresnel's biprism, scatter plate, Fizeau, Mach-Zehnder, Fabry-Perot,Laser Unequal Path, or Linnik interferometer. The interferometer maycomprise a fiber optic gyroscope, or a Zernike phase contrastmicroscope.

The sensor (e.g., optical, or temperature) may be any sensor describedin patent application number PCT/US15/65297, filed on Dec. 11, 2015,titled “FEEDBACK CONTROL SYSTEMS FOR THREE-DIMENSIONAL PRINTING,” whichis incorporated by reference in its entirety.

In some embodiments, the 3D object is supported during the 3D printing.For example, the 3D object may be supported by the base. For example,the 3D object may be anchored to the enclosure (e.g., to the base). The3D object may comprise auxiliary supports. The auxiliary support may bethe enclosure (e.g., the base) and/or structures that connect the 3Dobject to the enclosure (e.g., the base) and are not part of theintended (e.g., desired) 3D object. The 3D object may be devoid ofauxiliary supports. The 3D object may be supported by at least a portionof a fused material bed. The fused material bed (or a portion thereof)may or may not fully enclose (e.g., surround) the 3D object. The 3Dobject may be suspended in a material bed, which material bed comprisesflowable material (e.g., powder and/or liquid). The 3D object (e.g.,with or without auxiliary supports) may be floating in the material bedwithout being anchored to the enclosure (e.g., to the base). In someembodiments, the 3D object is devoid of auxiliary supports.

In some embodiments, the 3D object may comprises a reduced amount ofconstraints (e.g., supports) during the 3D printing. The reduced amountmay be relative to prevailing 3D printing methodologies (e.g.,respective methodologies). The 3D object may be less constraint (e.g.,relative to prevailing 3D printing methodologies). The 3D object may beconstraintless (e.g., supportless) during the 3D printing.

In some embodiments, the control includes imaging a surface. The imagingmay include stills or video imaging. The imaging may be at a directionperpendicular to the average or median plane of the exposed layer of thematerial bed. The imaging may be at a non-perpendicular direction to theaverage or median plane of the exposed layer of the material bed. Theimaging may be at a grazing angle with respect to the average or medianplane of the exposed layer of the material bed. The imaging may bedetected at an acute angle of at least about 1°, 5°, 10°, 15°, 20°, 30°,40°, 50°, 60°, 70°, or 80° relative to the average or mean plane of theexposed surface of the material bed. The symbol “°” designates the worddegrees. The imaging may be detected at an acute angle of at most about1°, 5°, 10°, 15°, 20°, 30°, 40°, 50°, 60°, 70°, or 80° relative to theaverage or mean plane of the exposed surface of the material bed. Theimaging may be detected at an acute angle between any of theabove-mentioned angles (e.g., from about 1° to about 80°, from about 1°to about 40°, or from about 40° to about 80°) relative to the average ormean plane of the exposed surface of the material bed.

In some examples, the imaging is performed during the formation of the3D object. The control may include processing the images obtained fromthe one or more sensors. The processing may comprise image processing.The image processing may reveal a variation in the surface (e.g.,planarity thereof). The revealed variation may trigger a modulation ofat least one function of (e.g., component participating in) the 3Dprinting process. The at least one functions of the 3D printing processmay comprise one or more characteristics of the energy beam as disclosedherein.

In some embodiments, the imaging comprises use of one or more imagingdevices (e.g., cameras). The control may comprise use of a positionsensor. The position sensor may comprise an absolute position sensor.The position sensor may comprise a relative position sensor. The positonsensor may be a metrological sensor. The relative position sensor maytake into account a comparison between two or more images of thesurface, which images are taken at different (e.g., known) times.

In some embodiments, the sensor comprises projecting a sensing energybeam. FIG. 3 shows an example of a 3D printer 360 that includes a sensorthat includes parts 317 (emitter) and 318 (receiver), which sensor(e.g., part 317) emits a sensing energy beam towards the exposed surface308 of the material bed 304. The sensing energy beam may be projectedfrom a direction above the exposed layer of the material bed (e.g., frompart 317). Above may be in a direction opposite to the direction of thegravitational force, platform (e.g., substrate 309 and/or base 302),and/or bottom of the enclosure (e.g., 305). The direction above theexposed layer may form an angle with the exposed layer. The angle may be(e.g., substantially) perpendicular. The angle may be acute. In someexamples, the sensor is disposed above the exposed layer of the materialbed (e.g., FIG. 3, sensor parts 317 (emitter) and 318 (receiver)). Insome embodiments, the sensor is disposed at the sides of the enclosure(e.g., FIG. 4, sensor parts 417 and 418). The sensor may be disposed atthe ceiling of the enclosure (e.g., FIG. 3, sensor parts 317 and 318).In some embodiments, parts of the sensor may be disposed at the sides ofthe enclosure, and other parts may be disposed at the ceiling of theenclosure. The sensor may be disposed within the enclosure (e.g., FIG.3, sensor parts 317 and 318). The sensor may be disposed outside of theenclosure. At least a part of the sensor may be disposed within and/oroutside the walls of the enclosure. At least a part of the sensor may bedisposed within the enclosure. Within the walls of the enclosure mayrefer to a situation where the part may form an integral part of thewall(s). The walls may comprise the side walls, the ceiling, or thebottom of the enclosure. Within the enclosure may refer to within theinterior of the enclosure. The sensing energy beam may be projected froma direction on the sides of the enclosure (e.g., 407). FIG. 4 shows anexample of a 3D printer 400 that includes a sensor comprising parts 417(emitter) and 418 (receiver). In the example of FIG. 4, the sensingenergy beam is emitted from the side of the enclosure (e.g., from part417). The sensing energy beam may be projected from a direction residingon the ceiling of the enclosure (e.g., FIG. 3, from part 317). Theceiling may or may not be substantially parallel to the exposed layer ofthe material bed, to the substrate, and/or to the bottom of theenclosure. The sensing energy beam may be projected from a directionresiding on the sides of the enclosure (e.g., FIG. 4, from part 417).The sides may be substantially perpendicular to the exposed layer of thematerial bed, to the substrate, and/or to the bottom of the enclosure.

In some embodiments, the sensor may sense radiation (e.g.,electromagnetic radiation) from a surface (e.g., exposed surface of thematerial bed, or of the 3D object), which radiation progresses to adirection above the exposed layer of the material bed. FIG. 3 shows anexample of a 3D printer 360, where the radiation 320 is projected fromthe exposed surface 308 of the material bed 304 towards the ceiling ofthe enclosure 300 and detected in the sensor part 318 (e.g., thereceiver). The direction above the exposed layer may be at an anglerelative to the exposed layer of the material bed. The angle may be(e.g., substantially) perpendicular. The angle may be acute. The sensormay sense radiation from a surface, which radiation progresses towardsthe sides of the enclosure. FIG. 4 shows an example where the radiation420 is projected from the exposed surface 408 of the material bed 404towards the side of the enclosure 407 and detected in the sensor part418 (e.g., the receiver). The sensor may sense radiation from a surface,which radiation progresses towards the ceiling of the enclosure.

In some embodiments, the radiation sensed by the sensor is that of thetransforming energy, which is reflected from the target surface.

The enclosure may comprise a window. The window may be an opticalwindow. FIG. 1 shows an example of an 3D printer 100 having an enclosurecomprising an optical window 115. The optical window may allow radiationfrom the surface to pass through (e.g., without substantial alterationand/or loss). The optical window may allow the sensing energy beamand/or the transforming energy beam to travel through (e.g., withoutsubstantial alteration and/or loss).

The sensor has a resolution. The resolution of the sensor may be lower(e.g., coarser) than the average or mean FLS of the particulate materialforming the material bed (e.g., powder particles in the powder bed).Lower may be by at least about 1%, 5%, 10%, 20%, 30%, 40%, 50%, 60%,70%, 80%, or 90% of the average or mean FLS of the particulate materialin the material bed. Lower may be by at most about 1%, 5%, 10%, 20%,30%, 40%, 50%, 60%, 70%, 80%, or 90% of the average or mean FLS of theparticulate material in the material bed. Lower may be by any valuebetween the afore-mentioned percentage values (e.g., from about 1% toabout 90%, from about 1% to about 50%, or from about 40% to about 90%)of the average or mean FLS of the particulate material in the materialbed. Lower by a value from about 1% to about 90% of the average or meanFLS of the particulate material in the material bed, means that theresolution of the sensor may be from 101% to 190% of the average or meanFLS of the particulate material in the material bed respectively.

In some embodiments, the sensor detects one or more movements that are afraction of the average or mean FLS of the particular material in thematerial bed (e.g., powder particles in the powder bed). The fractionmay be at least about 1%, 5%, 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, or90% of the average or mean FLS of the particulate material in thematerial bed. The fraction may be at most about 1%, 5%, 10%, 20%, 30%,40%, 50%, 60%, 70%, 80%, or 90% of the average or mean FLS of theparticulate material in the material bed. The fraction may be any valuebetween the afore-mentioned percentage values (e.g., from about 1% toabout 90%, from about 1% to about 50%, or from about 40% to about 90%)of the average or mean FLS of the particulate material.

In some embodiments, the control system (e.g., computing device) tracksthe position alteration that is detected at the surface. As a reactionto the position alteration, the controller may direct adjustment of oneor more functions of the 3D printing (e.g., using a software). Forexample, the controller may direct adjustment (e.g., alteration) of oneor more characteristics of the transformation (e.g., fusion) operation.The controller may direct adjustment (e.g., alteration) of at least onefunction of at least one mechanism based on the position alteration. Theadjustment may be before or during formation of a subsequent portion ofthe 3D object. For example, the controller may direct adjustment of oneor more characteristics of the transforming energy beam.

In some embodiments, the sensor measures a fraction of the surface. Insome embodiments, the sensor measures the entire surface (e.g., entireprotruding surface, entire exposed surface of the material bed, and/orentire target surface). The controller may take into account thepositions (whether altered or non-altered) in the entire surface. Thecontroller may take into account the sensor measurement of a fraction ofthe surface. The fraction may comprise an area of at least about 1 mm²,2 mm², 3 mm², 4 mm², 5 mm², 6 mm², 8 mm², 9 mm², 10 mm², 50 mm², 100mm², or 1000 mm². The fraction may comprise an area of at most about 1mm², 2 mm², 3 mm², 4 mm², 5 mm², 6 mm², 8 mm², 9 mm², 10 mm², 50 mm²,100 mm², 1000 mm², or of at least the entire exposed are of the materialbed. The fraction may comprise an area of any value between the aforementioned values (e.g., from about 1 mm² to about 1000 mm², from about 1mm² to about 5 mm², from about 5 mm² to about 10 mm², from about 10 mm²to about 50 mm², from about 50 mm² to about 1000 mm², or from about 1mm² to about the entire exposed surface area of the material bed).

In some embodiments, the controller takes into account sensormeasurements that are distant from the position at which thetransforming energy beam interacts with the material bed (e.g., theirradiated position). Distant can be at most about the edge of the lastformed layer of hardened material. Distant can be at the vicinity of theedge of the last formed layer of transformed (e.g., and/or hardened)material. Distant can be at least about 1 mm, 2 mm, 3 mm, 4 mm, 5 mm, 6mm, 7 mm, 8 mm, 9 mm, or 10 mm from the center of the transformingenergy beam footprint on the exposed surface of the material bed.Distant can be at most about 1 mm, 2 mm, 3 mm, 4 mm, 5 mm, 6 mm, 7 mm, 8mm, 9 mm, or 10 mm from the center of the transforming energy beamfootprint on the exposed surface of the material bed. Distant can be anyvalue between the afore-mentioned values (e.g., from about 1 mm to about10 mm, from about 1 mm to about 5 mm, or from about 5 mm to about 10 mm)relative to the center of the transforming energy beam footprint on theexposed surface of the material bed.

In some embodiments, the controller may takes into account one or moresensor measurements that are in the vicinity of a position of an edge ofthe last formed layer of hardened material. In the vicinity of theposition of the edge of the last formed layer of hardened material canbe at least about 1 mm, 2 mm, 3 mm, 4 mm, 5 mm, 6 mm, 7 mm, 8 mm, 9 mm,or 10 mm. In the vicinity of the position of the edge of the last formedlayer of hardened material can be at most about 1 mm, 2 mm, 3 mm, 4 mm,5 mm, 6 mm, 7 mm, 8 mm, 9 mm, or 10 mm. In the vicinity of the positionof the edge of the last formed layer of hardened material can be anyvalue between the afore-mentioned values (e.g., from about 1 mm to about10 mm, from about 1 mm to about 5 mm, or from about 5 mm to about 10mm). The sensor may sense the positions and/or areas that are taken intoaccount by the controller.

In some embodiments, the sensor conducts frequent measurements. Thesensor may conduct measurements at a frequency of at least about every 1second (sec), 2 sec, 3 sec, 4 sec, 4 sec, 5 sec, 6 sec, 7 sec, 8 sec, 9sec, 10 sec, 15 sec, 20 sec, 25 sec, 30 sec, 35 sec, 40 sec, 45 sec, 50sec, 60 sec, 70 sec, 75 sec, 80 sec, 90 sec, 95 sec, or 100 sec. Thesensor may conduct measurements at a frequency of at most about every 1sec, 2 sec, 3 sec, 4 sec, 4 sec, 5 sec, 6 sec, 7 sec, 8 sec, 9 sec, 10sec, 15 sec, 20 sec, 25 sec, 30 sec, 35 sec, 40 sec, 45 sec, 50 sec, 60sec, 70 sec, 75 sec, 80 sec, 90 sec, 95 sec, or 100 sec. The sensor mayconduct measurements at a frequency of any of the above-mentionedfrequencies (e.g., from about every 1 sec to about every 100 sec, fromabout every 5 sec, to about every 50 sec, from about every 5 sec toabout every 30 sec, from about every 30 sec to about every 50 sec, fromabout every 20 sec to about every 40 sec, or from about every 50 sec toabout every 100 sec). The controller may be programmed to direct takinginto account the measurements at a corresponding frequency. Thecontroller may be programmed to direct performing an image processing ofthe measurements at a corresponding frequency. The controller may beprogrammed to direct changing one or more functions of the 3D printingprocess (e.g., transforming energy beam characteristics) at acorresponding frequency.

In some embodiments, the image processing provides a positional map ofat least a fraction of the surface. The positional map may comprisevertical, horizontal, or angular (e.g., planar or compound) positions.The positional map may be provided at any of the frequencies mentionedherein. The positional map may be provided at a frequency of at leastabout 5 times/second (*/sec), 10 */sec, 20 */sec, 30 */sec, 40 */sec, 50*/sec, 60 */sec, 70 */sec, 80 */sec, 90 */sec, or 100 */sec. Thepositional map may be provided at a frequency of at most about 5 */sec,10 */sec, 20 */sec, 30 */sec, 40 */sec, 50 */sec, 60 */sec, 70 */sec, 80*/sec, 90 */sec, or 100 */sec. The positional map may be provided at afrequency between any of the afore-mentioned frequencies (e.g., fromabout 5 */sec to about 100 */sec, from about 5 */sec to about 50 */sec,from about 50 */sec to about 100 */sec, or from about 10 */sec to about1000 */sec). The character “*” designates the mathematical operation“times.”

In some embodiments, the radiative energy is reflected from a targetsurface (e.g., exposed surface of at least a portion of the materialbed, or exposed surface of at least a portion of a 3D object). The 3Dobject may be embedded (e.g., buried) in the material bed. FIG. 16 showsan example of a 3D object 1600 that is completely embedded in thematerial bed 1610. FIG. 14 shows an example of a 3D object 1400 that ispartially embedded in the material bed 1410, and includes a portion thatprotrudes (e.g., sticks out) of the exposed surface 1412 of the materialbed by a distance 1413.

In some embodiments, the radiative energy can be detected by an opticaldetector. The radiative energy can be detected by an imaging device(e.g., camera) and/or by a spectrum analyzer. The controller may varyone or more characteristics of the transforming energy beam based on anoutput of the sensor. The controller may vary one or more functions(e.g., characteristics) of at least one mechanism involved in the 3Dprinting (e.g., transforming energy source, scanner, layer dispensingmechanism, or any combination thereof) based on an output of the sensor.The characteristics of the transforming energy beam may comprise powerper unit area, speed, cross section, or average footprint on the exposedsurface of the material bed. The controller may comprise performingimage analysis (e.g., image processing) using the output of the sensor(e.g., optical sensor, and/or imaging device), to provide a result. Theimage analysis may be conducted by a non-transitory computer readablemedium. The radiative energy may be sensed (e.g., imaged) from one ormore angles (e.g., sequentially, simultaneously, or at random). Theresult may be used in the control of at least one functions of the 3Dprinting (e.g., altering the transforming energy beam (e.g., to alterthe at least one of its characteristics)), and/or altering at least onemechanism associated with the transforming energy beam. The mechanismassociated with the transforming energy beam may be an optical mechanism(e.g., comprising a scanner, lens or a mirror), and/or an energy source.The result may be used in evaluating one or more positons at the targetsurface. The result may be used in evaluating the height at variouspositions of the target surface. The height may be relative to a knownheight (e.g., height baseline, or predetermined height), to theplatform, the floor of the processing chamber, or to other positionswithin the 3D object or within the target surface. The result may beused in the evaluation of the deviation from planarity of the targetsurface. The result may provide a vertical and/or horizontal heightprofile of the target surface. The result may provide a height and/orplanarity profile of the target surface. The resolution of the heightand/or planarity profile may correspond to the FLS of a cross section ofthe sensing energy beam, or the FLS of a footprint of the sensing energybeam on the target surface. The resolution of the height and/orplanarity profile may correspond to the sensor resolution. Theresolution of the height and/or planarity profile may correspond to theFLS of a cross section of the transforming energy beam, or the FLS of afootprint of the transforming energy beam on the target surface.

In some embodiments, the radiative energy beam sensed by the metrology(e.g., position) sensor is the reflection of the transforming energybeam from the target surface. In some examples, the radiative energysensed by the metrology sensor is an energy beam different from areflection of the transforming energy beam. For example, the radiativeenergy may be a reflection of the sensing energy beam from the targetsurface. The detector (e.g., FIG. 3, 318) may be coupled to thecontroller. For example, the detector (e.g., FIG. 3, 318) may be coupledto the computer (e.g., through a communication channel). The controllermay analyze the signal detected by the detector. The output of thedetector may be taken into account by the systems, software, and/orapparatuses (e.g., by the controller) to direct alteration of at leastone function of the 3D printing as a result of an analysis of thedetector output. The at least one function may include at least onecharacteristic of the transforming energy beam.

In some embodiments, the optical detector (e.g., temperature detector)comprises an optical setup. The optical setup may comprise a lensarrangement. The optical setup may comprise a beam splitter. Thedetector may comprise a focusing lens. The detector may view (e.g.,detect) a focused point (e.g., of the exposed surface of the materialbed). The optical setup may be the same optical setup used by thetransforming energy beam (e.g., through which the transforming energybeam travels). The optical setup may be different from the optical setupused by the transforming energy beam. The sensing (e.g., and detecting)energy beam and the transforming energy beam may be confocal. Thesensing energy beam and the transforming energy beam may travel indifferent paths. The sensing energy beam and transforming energy beammay travel through the same different optical windows. The sensingenergy beam and the transforming energy beam may be translated by thesame or by different scanners. For example, the transforming energy beammay be translated by a first scanner, and the sensing energy beam may betranslated by a second scanner, wherein the second scanner tracks (e.g.,chases) the first energy beam. The detector (e.g., optical detector) maycontrol (e.g., monitor and/or regulate) the reflected energy from thetarget surface (e.g., exposed surface of the material bed). The detectorenergy beam (e.g., the reflected sensing energy beam from the targetsurface) may be coaxial or non-coaxial with a reflection of thetransforming energy beam. The detected energy beam that is reflectedfrom the target surface (e.g., from the exposed surface of the materialbed and/or forming layer of hardened material) may be used to imagethese respective exposed surfaces.

In some embodiments, the optical sensor is used for temperaturemeasurements and/or for metrological measurements. The temperaturesensor and/or positional sensor may comprise the optical sensor. Theoptical sensor may include an analogue device (e.g., CCD). The opticalsensor may include a p-doped metal-oxide-semiconductor (MOS) capacitor,charge-coupled device (CCD), active-pixel sensor (APS),micro/nano-electro-mechanical-system (MEMS/NEMS) based sensor, or anycombination thereof The APS may be a complementarymetal-oxide-semiconductor (CMOS) sensor. The MEMS/NEMS sensor mayinclude a MEMS/NEMS inertial sensor. The MEMS/NEMS sensor may be basedon silicon, polymer, metal, ceramics, or any combination thereof Theoptical sensor may comprise laser scanner, or an interferometer. Theinterferometer may comprise a coherent (e.g., white) light, or partialcoherence interferometer. The temperature sensor (e.g., thermal sensor)may sense a IR radiation (e.g., photons). The thermal sensor may sense atemperature of at least one melt pool. The metrology sensor may comprisea sensor that measures the FLS (e.g., depth) of at least one melt pool.The transforming energy beam and the sensing energy beam (e.g., thermalsensor beam and/or metrology sensor energy beam) may be focused on(e.g., substantially) the same position. The transforming energy beamand the sensing energy beam (e.g., thermal sensor beam and/or metrologysensor energy beam) may be confocal.

The methods, systems, software, and/or apparatuses described herein maytake into account (e.g., by a controller) sensor signals from at least aportion of the surface (e.g., of the exposed material bed, and/or of theprotruding 3D object from the material bed). The signals may correspondto positional signals. The positions may include vertical, horizontal,and/or angular positions. The signals may correspond to height and/orlateral differences of corresponding surface positions.

In some embodiments, the methods, systems, apparatuses, and/or softwaredescribed herein may take into account at least one or more sensormeasurements. As a consequence of the measurements, the controller maydirect alteration of one or more functions of the 3D printing process(e.g., of the transforming energy beam). The direction may include theuse of a software that is coupled to the sensor through a firstcommunication channel The software may be coupled to at least onefunction of the 3D printer through a second communication channel Thefirst and second communication channels may be the same communicationchannel or different communication channels.

In some embodiments, the methods, systems, apparatuses, and/or softwaredescribed herein may take into account at least one or more temperaturesensor measurements. As a consequence of the temperature measurements,the controller may direct alteration of one or more functions of the 3Dprinting process (e.g., of the transforming energy beam). Thetemperature measurements may comprise temperature measurements of thesurface (e.g., target surface, e.g., exposed surface of the materialbed, and/or of the 3D object). The temperature measurements may includecontact or non-contact temperature measurements. The controller may takeinto account both the positional sensor measurements and the temperaturesensor measurements. As a consequence of the temperature measurements,one or more functions of the 3D printing process (e.g., of thetransforming energy beam) may be altered (e.g., directed by thecontroller). The temperature measurements may comprise temperaturemeasurements of one or more positions of the surface.

In some embodiments, the methods, systems, software, and/or apparatusesdescribed herein may consider at least one or more measurements of thetransforming energy beam. The measurements may comprise measuring thecross section of the energy beam (e.g., in a direction perpendicular toits propagation), footprint on the exposed surface of the material bed,energy flux, energy per unit area, dwell time, delay time (e.g., beamoff time), pulsing beam frequency, wavelength, or velocity at which thetransforming energy beam travels on the exposed surface of the materialbed. The measurements may comprise measuring the path (e.g., hatch)spacing of the transforming energy beam path traveled on the targetsurface (e.g., exposed surface of the material bed). For example, thecontroller may take into account at least one or more measurements ofthe transforming energy beam characteristics. As a consequence of thetransforming energy beam characteristics measurement(s), the controllermay direct alteration of one or more functions of the 3D printingprocess (e.g., of and/or associated with the transforming energy beam).The controller may take into account two or more of (i) positionalsensor measurements, (ii) temperature sensor measurements, (iii)energy-source power measurement, and (iv) measurement of at least onecharacteristic of the transforming energy beam. For example, themethods, systems, software and/or apparatuses may consider both thepositional sensor measurements and the transforming energy beamcharacteristics measurements. As a consequence of the transformingenergy beam characteristics measurements, one or more functions of the3D printing process (e.g., of the and/or associated with thetransforming energy beam) may be altered. The alteration may be directedby the controller. For example, the alteration may be using a software.For example, the alteration may be through a communication channel

The methods, systems, apparatuses, and/or software described herein maycontrol (e.g., regulate) the deformation of at least a portion of the 3Dobject by controlling at least one function of the 3D printing (e.g., atleast one characteristic of the transforming energy beam and/or itsenergy source) while measuring a position of the surface and/or whilemeasuring the temperature of the surface. The control may be during theformation of the 3D object. The control may be during the 3D printingprocess. The control may be real-time control. The control may be insitu control. The control may be at least during the transformingoperation. The control may be at least during the hardening of thetransformed material. The control may be at least during the formationof a hardened layer (or a portion thereof) as part of the 3D object.

In some embodiments, the material (e.g., pre-transformed material,transformed material, or hardened material) comprises elemental metal,metal alloy, ceramics, or an allotrope of elemental carbon. Theallotrope of elemental carbon may comprise amorphous carbon, graphite,graphene, diamond, or fullerene. The fullerene may be selected from thegroup consisting of a spherical, elliptical, linear, and tubularfullerene. The fullerene may comprise a buckyball or a carbon nanotube.The ceramic material may comprise cement. The ceramic material maycomprise alumina. The material may comprise sand, glass, or stone. Insome embodiments, the material may comprise an organic material, forexample, a polymer or a resin. The organic material may comprise ahydrocarbon. The polymer may comprise styrene. The organic material maycomprise carbon and hydrogen atoms, carbon and oxygen atoms, carbon andnitrogen atoms, carbon and sulfur atoms, or any combination thereof. Insome embodiments, the material may exclude an organic material (e.g.,polymer). The polymer may comprise plastic, polyurethane, or wax. Thepolymer may comprise a resin. The material may comprise a solid or aliquid. In some embodiments, the material may comprise a silicon-basedmaterial, for example, silicon based polymer or a resin. The materialmay comprise an organosilicon-based material. The material may comprisesilicon and hydrogen atoms, silicon and carbon atoms, or any combinationthereof. In some embodiments, the material may exclude a silicon-basedmaterial. The material may comprise a particulate material. Theparticulate material may comprise solid or semi-solid (e.g., gel). Theparticulate material may comprise powder. The powder material maycomprise a solid. The powder material may be coated by a coating (e.g.,organic coating such as the organic material (e.g., plastic coating)).The material may be devoid of organic material. In some examples, thematerial may not be coated by organic and/or silicon based materials.The liquid material may be compartmentalized into reactors, vesicles, ordroplets. The compartmentalized material may be compartmentalized in oneor more layers. The material may be a composite material comprising asecondary material. The secondary material can be a reinforcing material(e.g., a material that forms a fiber). The reinforcing material maycomprise a carbon fiber, Kevlar®, Twaron®, ultra-high-molecular-weightpolyethylene, or glass fiber. The material can comprise powder (e.g.,granular material) or wires.

In some embodiments, the pre-transformed material comprises a powdermaterial. The pre-transformed material may comprise a solid material.The pre-transformed material may comprise one or more particles orclusters. The term “powder,” as used herein, generally refers to a solidhaving fine particles. Powders may be granular materials. The powderparticles may comprise micro particles. The powder particles maycomprise nanoparticles. In some examples, a powder comprising particleshaving an average FLS of at least about 5 nanometers (nm), 10 nm, 20 nm,30 nm, 40 nm, 50 nm, 100 nm, 200 nm, 300 nm, 400 nm, 500 nm, 1 μm, 5 μm,10 μm, 15 μm, 20 μm, 25 μm, 30 μm, 35 μm, 40 μm, 45 μm, 50 μm, 55 μm, 60μm, 65 μm, 70 μm, 75 μm, 80 μm, or 100 μm. The particles comprising thepowder may have an average FLS of at most about 100 μm, 80 μm, 75 μm, 70μm, 65 μm, 60 μm, 55 μm, 50 μm, 45 μm, 40 μm, 35 μm, 30 μm, 25 μm, 20μm, 15 μm, 10 μm, 5 μm, 1 μm, 500 nm, 400 nm, 300 nm, 200 nm, 100 nm, 50nm, 40 nm, 30 nm, 20 nm, 10 nm, or 5 nm. In some cases, the powder mayhave an average fundamental length scale between any of the values ofthe average particle fundamental length scale listed above (e.g., fromabout 5 nm to about 100 μm, from about 1 μm to about 100 μm, from about15 μm to about 45 μm, from about 5 μm to about 80 μm, from about 20 μmto about 80 μm, or from about 500 nm to about 50 μm). The powder can becomposed of individual particles. The individual particles can bespherical, oval, prismatic, cubic, wires, or irregularly shaped. Theparticles can have a FLS. The powder can be composed of a homogenouslyshaped particle mixture such that all of the particles havesubstantially the same shape and FLS magnitude within at most 1%, 5%,8%, 10%, 15%, 20%, 25%, 30%, 35%, 40%, 50%, 60%, or 70%, distribution ofFLS. In some cases, the powder can be a heterogeneous mixture such thatthe particles have variable shape and/or FLS magnitude.

In some embodiments, at least a portion of the layer can be transformedto a transformed material (e.g., using an energy beam) that maysubsequently form at least a fraction (also used herein “a portion,” or“a part”) of a hardened (e.g., solidified) 3D object. At times a layerof transformed or hardened material may comprise a cross section of a 3Dobject (e.g., a horizontal cross section). The layer may correspond to across section of a desired 3D object. At times a layer of transformed orhardened material may comprise a deviation from a cross section of amodel of a requested 3D object. The deviation may include verticaland/or horizontal deviation. A pre-transformed material may be a powdermaterial. In some embodiments, the pre-transformed material is depositedabove a platform in (e.g., planar) one or more planar layers. Apre-transformed material layer (or a potion thereof) can have athickness (e.g., layer height) of at least about 0.1 micrometer (um),0.5 μm, 1.0 μm, 10 μm, 50 μm, 100 μm, 150 μm, 200 μm, 300 μm, 400 μm,500 μm, 600 μm, 700 μm, 800 μm, 900 μm, or 1000 μm. A pre-transformedmaterial layer (or a potion thereof) can have a thickness of at mostabout 1000 μm, 900 μm, 800 μm, 700 μm, 600 μm, 500 μm, 450 μm, 400 μm,350 μm, 300 μm, 250 μm, 200 μm, 150 μm, 100 μm, 75 μm, 50 μm, 40 μm, 30μm, 20 μm, 5 μm, 1 μm, or 0.5 μm. A pre-transformed material layer (or apotion thereof) may have any value in between the afore-mentioned layerthickness values (e.g., from about 1000 μm to about 0.1 μm, 800 μm toabout 1 μm, from about 600 μm to about 20 μm, from about 300 μm to about30 μm, or from about 1000 μm to about 10 μm). At times, the controllerdirects adjustment of the thickness (e.g., height. E.g., FIG. 15, thedistance from surface 1512 to surface 1514) of a layer ofpre-transformed material (e.g., that is disposed to form the materialbed). The material composition of at least one layer within the materialbed may differ from the material composition within at least one otherlayer in the material bed. The difference (e.g., variation) may comprisedifference in crystal or grain structure. The variation may comprisevariation in grain orientation, material density, degree of compoundsegregation to grain boundaries, degree of element segregation to grainboundaries, material phase, metallurgical phase, material porosity,crystal phase, or crystal structure. The microstructure of the printedobject may comprise planar structure, cellular structure, columnardendritic structure, or equiaxed dendritic structure. The controller maydirect formation of a certain type of metallurgical microstructure to be(e.g., predominantly) formed during the 3D printing. The systems,apparatuses, and/or methods may form a desired metallurgical structureduring (e.g., a specific stage of) the 3D printing.

In some examples, the pre-transformed material in one or more layers ofthe material bed, differs from the pre-transformed material in adifferent one or more layers of the material bed. For example, thepre-transformed materials of at least one layer in the material bed maydiffer in the FLS of its particles (e.g., powder particles) from the FLSof the pre-transformed material within at least one other layer in thematerial bed. For example, the pre-transformed materials of at least onelayer in the material bed may differ in material type and/or compositionfrom the material type and/or composition (respectively) of thepre-transformed material within at least one other layer in the materialbed. A layer may comprise two or more material types at any combination.For example, two or more elemental metals, two or more metal alloys, twoor more ceramics, two or more allotropes of elemental carbon. Forexample, an elemental metal and a metal alloy, an elemental metal and aceramic, an elemental metal and an allotrope of elemental carbon, ametal alloy and a ceramic, a metal alloy and an allotrope of elementalcarbon, or a ceramic and an allotrope of elemental carbon. All thelayers of pre-transformed material deposited during the 3D printingprocess may be of (e.g., substantially) the same material type and/orcomposition. In some instances, a metal alloy is formed in situ duringthe process of transforming at least a portion of the material bed. Insome instances, a metal alloy is not formed in situ during the processof transforming at least a portion of the material bed. In someinstances, a metal alloy is formed prior to the process of transformingat least a portion of the material bed. In a multiplicity (e.g.,mixture) of pre-transformed (e.g., powder) materials, onepre-transformed material may be used as support (i.e., supportivepowder), as an insulator, as a cooling member (e.g., heat sink), or asany combination thereof.

In some instances, adjacent components in the material bed are separatedfrom one another by one or more intervening layers. In an example, afirst layer is adjacent to a second layer when the first layer is indirect contact with the second layer. In another example, a first layeris adjacent to a second layer when the first layer is separated from thesecond layer by at least one layer (e.g., a third layer). Theintervening layer may be of any layer size.

In some embodiments, the pre-transformed material (e.g., powdermaterial) is chosen such that the material is (or forms in situ) thedesired and/or otherwise predetermined material for the 3D object. Alayer of the 3D object may comprise a single type of material. Forexample, a layer of the 3D object may comprise a single elemental metaltype, or a single metal alloy type. In some examples, a layer within the3D object may comprise several types of material (e.g., an elementalmetal and an alloy, an alloy and ceramics, or an alloy and an allotropeof elemental carbon). In certain embodiments, each type of materialcomprises only a single member of that type. For example: a singlemember of elemental metal (e.g., iron), a single member of metal alloy(e.g., stainless steel), a single member of ceramic material (e.g.,silicon carbide or tungsten carbide), or a single member (e.g., anallotrope) of elemental carbon (e.g., graphite). In some cases, a layerof the 3D object comprises more than one type of material. In somecases, a layer of the 3D object comprises more than one member of amaterial type.

The elemental metal can be an alkali metal, an alkaline earth metal, atransition metal, a rare-earth element metal, or another metal. Thealkali metal can be Lithium, Sodium, Potassium, Rubidium, Cesium, orFrancium. The alkali earth metal can be Beryllium, Magnesium, Calcium,Strontium, Barium, or Radium. The transition metal can be Scandium,Titanium, Vanadium, Chromium, Manganese, Iron, Cobalt, Nickel, Copper,Zinc, Yttrium, Zirconium, Platinum, Gold, Rutherfordium, Dubnium,Seaborgium, Bohrium, Hassium, Meitnerium, Ununbium, Niobium, Iridium,Molybdenum, Technetium, Ruthenium, Rhodium, Palladium, Silver, Cadmium,Hafnium, Tantalum, Tungsten, Rhenium, or Osmium. The transition metalcan be mercury. The rare-earth metal can be a lanthanide, or anactinide. The lanthanide metal can be Lanthanum, Cerium, Praseodymium,Neodymium, Promethium, Samarium, Europium, Gadolinium, Terbium,Dysprosium, Holmium, Erbium, Thulium, Ytterbium, or Lutetium. Theactinide metal can be Actinium, Thorium, Protactinium, Uranium,Neptunium, Plutonium, Americium, Curium, Berkelium, Californium,Einsteinium, Fermium, Mendelevium, Nobelium, or Lawrencium. The othermetal can be Aluminum, Gallium, Indium, Tin, Thallium, Lead, or Bismuth.

The metal alloy can be an iron based alloy, nickel based alloy, cobaltbased alloy, chrome based alloy, cobalt chrome based alloy, titaniumbased alloy, magnesium based alloy, copper based alloy, or anycombination thereof. The alloy may comprise an oxidation or corrosionresistant alloy. The alloy may comprise a super alloy (e.g., Inconel).The super alloy may comprise Inconel. For example, the super alloy maycomprise Inconel 600, 617, 625, 690, 718, or X-750. The nickel basealloy may comprise MAR-246. The metal (e.g., alloy or elemental) maycomprise an alloy used for applications in industries comprisingaerospace (e.g., aerospace super alloys), jet engine, missile,automotive, marine, locomotive, satellite, defense, oil & gas, energygeneration, semiconductor, fashion, construction, agriculture, printing,or medical. The metal (e.g., alloy or elemental) may comprise an alloyused for products comprising, devices, impellers, medical devices (human& veterinary), machinery, cell phones, semiconductor equipment,generators, engines, pistons, electronics (e.g., circuits), electronicequipment, agriculture equipment, motor, gear, transmission,communication equipment, computing equipment (e.g., laptop, cell phone,i-pad), air conditioning, generators, furniture, musical equipment, art,jewelry, cooking equipment, or sport gear. The metal (e.g., alloy orelemental) may comprise an alloy used for products for human and/orveterinary applications comprising implants, or prosthetics. The metalalloy may comprise an alloy used for applications in the fieldscomprising human and/or veterinary surgery, implants (e.g., dental), orprosthetics. The metal (e.g., alloy or elemental) may comprise an alloyused for products comprising a rotating part. The rotating part may beof a centrifugal pump, compressor, or other machine designed to move afluid (e.g., fuel) by rotation.

The alloy may include a superalloy. The alloy may include ahigh-performance alloy. The alloy may include an alloy exhibitingexcellent mechanical strength, resistance to thermal creep deformation,good surface stability, resistance to corrosion, resistance tooxidation, or any combination thereof. The alloy may include aface-centered cubic austenitic crystal structure. The alloy may compriseHastelloy, Inconel, Waspaloy, Rene alloy (e.g., Rene-80, Rene-77,Rene-220, or Rene-41), Haynes alloy, Incoloy, MP98T, TMS alloy, MTEK(e.g., MTEK grade MAR-M-247, MAR-M-509, MAR-M-R41, or MAR-M-X-45), orCMSX (e.g., CMSX-3, or CMSX-4). The alloy can be a single crystal alloy.

In some instances, the iron alloy comprises Elinvar, Fernico,Ferroalloys, Invar, Iron hydride, Kovar, Spiegeleisen, Staballoy(stainless steel), or Steel. In some instances, the metal alloy issteel. The Ferroalloy may comprise Ferroboron, Ferrocerium, Ferrochrome,Ferromagnesium, Ferromanganese, Ferromolybdenum, Ferronickel,Ferrophosphorus, Ferrosilicon, Ferrotitanium, Ferrouranium, orFerrovanadium. The iron alloy may comprise cast iron, or pig iron. Thesteel may comprise Bulat steel, Chromoly, Crucible steel, Damascussteel, Hadfield steel, High speed steel, HSLA steel, Maraging steel,Reynolds 531, Silicon steel, Spring steel, Stainless steel, Tool steel,Weathering steel, or Wootz steel. The high-speed steel may compriseMushet steel. The stainless steel may comprise AL-6XN, Alloy 20,celestrium, marine grade stainless, Martensitic stainless steel,surgical stainless steel, or Zeron 100. The tool steel may compriseSilver steel. The steel may comprise stainless steel, Nickel steel,Nickel-chromium steel, Molybdenum steel, Chromium steel,Chromium-vanadium steel, Tungsten steel, Nickel-chromium-molybdenumsteel, or Silicon-manganese steel. The steel may be comprised of anySociety of Automotive Engineers (SAE) grade steel such as 440F, 410,312, 430, 440A, 440B, 440C, 304, 305, 304L, 304L, 301, 304LN, 301LN,2304, 316, 316L, 316LN, 316, 316LN, 316L, 316L, 316, 317L, 2205, 409,904L, 321, 254SMO, 316Ti, 321H, or 304H. The steel may comprisestainless steel of at least one crystalline structure selected from thegroup consisting of austenitic, superaustenitic, ferritic, martensitic,duplex, and precipitation-hardening martensitic, or any combinationthereof. Duplex stainless steel may comprise lean duplex, standardduplex, super duplex, or hyper duplex. The stainless steel may comprisesurgical grade stainless steel (e.g., austenitic 316, martensitic 420,or martensitic 440). The austenitic 316 stainless steel may comprise316L, or 316LVM. The steel may comprise 17-4 Precipitation Hardeningsteel (e.g., type 630, a chromium-copper precipitation hardeningstainless steel, or 17-4PH steel).

The titanium-based alloy may comprise alpha alloy, near alpha alloy,alpha and beta alloy, or beta alloy. The titanium alloy may comprisegrade 1, 2, 2H, 3, 4, 5, 6, 7, 7H, 8, 9, 10, 11, 12, 13, 14, 15, 16,16H, 17, 18, 19, 20, 21, 2, 23, 24, 25, 26, 26H, 27, 28, 29, 30, 31, 32,33, 34, 35, 36, 37, 38, or higher. In some instances, the titanium basealloy comprises Ti-6Al-4V or Ti-6Al-7Nb.

The Nickel alloy may comprise Alnico, Alumel, Chromel, Cupronickel,Ferronickel, German silver, Hastelloy, Inconel, Monel metal, Nichrome,Nickel-carbon, Nicrosil, Nisil, Nitinol, or Magnetically “soft” alloys.The magnetically “soft” alloys may comprise Mu-metal, Permalloy,Supermalloy, or Brass. The brass may comprise Nickel hydride, Stainlessor Coin silver. The cobalt alloy may comprise Megallium, Stellite (e. g.Talonite), Ultimet, or Vitallium. The chromium alloy may comprisechromium hydroxide, or Nichrome.

The aluminum alloy may comprise AA-8000, Al—Li (aluminum-lithium),Alnico, Duralumin, Hiduminium, Kryron Magnalium, Nambe,Scandium-aluminum, or Y alloy. The magnesium alloy may compriseElektron, Magnox, or T-Mg—Al—Zn (Bergman phase) alloy.

The copper alloy may comprise Arsenical copper, Beryllium copper,Billon, Brass, Bronze, Constantan, Copper hydride, Copper-tungsten,Corinthian bronze, Cunife, Cupronickel, Cymbal alloys, Devarda's alloy,Electrum, Hepatizon, Heusler alloy, Manganin, Molybdochalkos, Nickelsilver, Nordic gold, Shakudo, or Tumbaga. The Brass may compriseCalamine brass, Chinese silver, Dutch metal, Gilding metal, Muntz metal,Pinchbeck, Prince's metal, or Tombac. The Bronze may comprise Aluminumbronze, Arsenical bronze, Bell metal, Florentine bronze, Guanin,Gunmetal, Glucydur, Phosphor bronze, Ormolu, or Speculum metal.

In some examples, the material (e.g., powder material) comprises amaterial, wherein the constituents of that material (e.g., atoms ormolecules) readily lose their outer shell electrons, resulting in afree-flowing cloud of electrons within their otherwise solidarrangement. In some examples the material is characterized in havinghigh electrical conductivity, low electrical resistivity, high thermalconductivity, and/or high density (e.g., as measured at ambienttemperature (e.g., R.T., or 20° C.)). The high electrical conductivitycan be at least about 1*10⁵ Siemens per meter (S/m), 5*10⁵ S/m, 1*10⁶S/m, 5*10⁶ S/m, 1*10⁷ S/m, 5*10⁷ S/m, or 1*10⁸ S/m. The symbol “*”designates the mathematical operation “times,” or “multiplied by.” Thehigh electrical conductivity can be any value between theafore-mentioned electrical conductivity values (e.g., from about 1*10⁵S/m to about 1*10⁸ S/m). The low electrical resistivity may be at mostabout 1*10⁻⁵ ohm times meter (Ω*m), 5*10⁻⁶ Ω*m, 1*10⁻⁶ Ω*m, 5*10⁻⁷ Ω*m,1*10⁻⁷ Ω*m, 5*10⁻⁸, or 1*10⁻⁸ Ω*m. The low electrical resistivity can beany value between the afore-mentioned electrical resistivity values(e.g., from about 1×10⁻⁵ Ω*m to about 1×10⁻⁸ Ω*m). The high thermalconductivity may be at least about 20 Watts per meters times degreesKelvin (W/mK), 50 W/mK, 100 W/mK, 150 W/mK, 200 W/mK, 205 W/mK, 300W/mK, 350 W/mK, 400 W/mK, 450 W/mK, 500 W/mK, 550 W/mK, 600 W/mK, 700W/mK, 800 W/mK, 900 W/mK, or 1000 W/mK. The high thermal conductivitycan be any value between the afore-mentioned thermal conductivity values(e.g., from about 20 W/mK to about 1000 W/mK). The high density may beat least about 1.5 grams per cubic centimeter (g/cm³), 2 g/cm³, 3 g/cm³,4 g/cm³, 5 g/cm³, 6 g/cm³, 7 g/cm³, 8 g/cm³, 9 g/cm³, 10 g/cm³, 11g/cm³, 12 g/cm³, 13 g/cm³, 14 g/cm³, 15 g/cm³, 16 g/cm³, 17 g/cm³, 18g/cm³, 19 g/cm³, 20 g/cm³, or 25 g/cm³. The high density can be anyvalue between the afore-mentioned density values (e.g., from about 1g/cm³ to about 25 g/cm³).

A metallic material (e.g., elemental metal or metal alloy) can comprisesmall amounts of non-metallic materials, such as, for example,comprising the elements oxygen, sulfur, or nitrogen. In some cases, themetallic material can comprise the non-metallic material (e.g., and/orelements) in a trace amount. A trace amount can be at most about 100000parts per million (ppm), 10000 ppm, 1000 ppm, 500 ppm, 400 ppm, 200 ppm,100 ppm, 50 ppm, 10 ppm, 5 ppm, or 1 ppm (on the basis of weight, w/w)of non-metallic material. A trace amount can comprise at least about 10ppt, 100 ppt, 1 ppb, 5 ppb, 10 ppb, 50 ppb, 100 ppb, 200 ppb, 400 ppb,500 ppb, 1000 ppb, 1 ppm, 10 ppm, 100 ppm, 500 ppm, 1000 ppm, or 10000ppm (based on weight, w/w) of non-metallic material (and/or elements). Atrace amount can be any value between the afore-mentioned trace amounts(e.g., from about 10 parts per trillion (ppt) to about 100000 ppm, fromabout 1 ppb to about 100000 ppm, from about 1 ppm to about 10000 ppm, orfrom about 1 ppb to about 1000 ppm).

The one or more layers within the 3D object may be substantially planar(e.g., flat). The planarity of the layer may be substantially uniform.The height of the layer at a position may be compared to an averageplane of that layer. The average plane may be defined by a least squaresplanar fit of the top-most part of the surface of the layer of hardenedmaterial. The average plane may be a plane calculated by averaging thematerial height at each point on the top surface of the layer ofhardened material. The deviation from any point at the surface of theplanar layer of hardened material may be at most 20% 15%, 10%, 5%, 3%,1%, or 0.5% of the height (e.g., thickness) of the layer of hardenedmaterial. The substantially planar one or more layers may have a largeradius of curvature. FIG. 7 shows an example of a vertical cross sectionof a 3D object 712 comprising planar layers (layers numbers 1-4) andnon-planar layers (e.g., layers numbers 5-6) that have a radius ofcurvature. FIGS. 7, 716 and 717 are super-positions of curved layer on acircle 715 having a radius of curvature “r.” The one or more layers mayhave a radius of curvature (e.g., substantially) equal to the radius ofcurvature of the layer surface. The radius of curvature may equalinfinity (e.g., when the layer is planar). The radius of curvature ofthe layer surface (e.g., all the layers of the 3D object) may have avalue of at least about 0.1 centimeter (cm), 0.2 cm, 0.3 cm, 0.4 cm, 0.5cm, 0.6 cm, 0.7 cm, 0.8 cm, 0.9 cm, 1 cm, 3 cm, 5 cm, 10 cm, 20 cm, 30cm, 40 cm, 50 cm, 60 cm, 70 cm, 80 cm, 90 cm, 1 meter (m), 1.5 m, 2 m,2.5 m, 3 m, 3.5 m, 4 m, 4.5 m, 5 m, 10 m, 15 m, 20 m, 25 m, 30 m, 50 m,or 100 m. The radius of curvature of the layer surface (e.g., all thelayers of the 3D object) may have any value between any of theafore-mentioned values of the radius of curvature (e.g., from about 0.1cm to about 100 m, from about 10 cm to about 90 m, from about 50 cm toabout 10 m, from about 5 cm to about 1 m, from about 50 cm to about 5 m,from about 5 cm to infinity, or from about 40 cm to about 50 m). In someexamples, the one or more layers may be included in a planar section ofthe 3D object, or may be a planar 3D object (e.g., a flat plane). Insome instances, part of at least one layer within the 3D object may haveany of the radii of curvature mentioned herein, which will designate theradius of curvature of that layer portion.

The 3D object may comprise a layering plane N of the layered structure.FIG. 10C shows an example of a 3D object having a layered structure,wherein 1005 shows an example of a side view of a plane, wherein 1001shows an example of a layering plane. The layering plane may be theaverage or mean plane of a layer of hardened material (as part of the 3Dobject). FIG. 8 shows an example of points X and Y on the surface of a3D object. In some embodiments, X is spaced apart from Y by theauxiliary feature spacing distance (e.g., as described herein). A sphereof radius XY that is centered at X may lack one or more auxiliarysupports or one or more auxiliary support marks that are indicative of apresence or removal of the one or more auxiliary support features (e.g.,after completion of the 3D printing). An acute angle between thestraight line XY and the direction normal to N may be from about 45degrees to about 90 degrees. The acute angle between the straight lineXY and the direction normal to the layering plane may be of the value ofthe acute angle alpha (e.g., as described herein). When the anglebetween the straight line XY and the direction of normal to N is greaterthan 90 degrees, one can consider the complementary acute angle. Thelayer structure may comprise any material(s) used for 3D printing. Alayer of the 3D structure can be made of a single material or ofmultiple materials. Sometimes one part of the layer may comprise onematerial, and another part may comprise a second material different thanthe first material. A layer of the 3D object may be composed of acomposite material. The 3D object may be composed of a compositematerial. The 3D object may comprise a functionally graded material(e.g., comprising a functionally graded microstructure).

In some embodiments, the generated 3D object may be generated with theaccuracy of at least about 5 μm, 10 μm, 15 μm, 20 μm, 25 μm, 30 μm, 35μm, 40 μm, 45 μm, 50 μm, 55 μm, 60 μm, 65 μm, 70 μm, 75 μm, 80 μm, 85μm, 90 μm, 95 μm, 100 μm, 150 μm, 200 μm, 250 μm, 300 μm, 400 μm, 500μm, 600 μm, 700 μm, 800 μm, 900 μm, 1000 μm, 1100 μm, or 1500 μm withrespect to a model of the 3D object (e.g., the desired 3D object) withrespect to the (virtual) model of a requested 3D object. With respect toa model of the 3D object, the generated 3D object may be generated withthe accuracy of any accuracy value between the afore-mentioned values(e.g., from about 5 μm to about 100 μm, from about 15 μm to about 35 μm,from about 100 μm to about 1500 μm, from about 5 μm to about 1500 μm, orfrom about 400 μm to about 600 μm).

The hardened layer of transformed material may deform. The deformationmay cause a vertical (e.g., height) and/or horizontal (e.g., widthand/or length) deviation from a desired uniformly planar layer. Thevertical and/or horizontal deviation of the surface of the layer ofhardened material from planarity may be at least about 100 μm, 90 μm, 80μm, 70 μm, 60 μm, 50 μm, 40 μm, 30 μm, 20 μm, 10 μm, or 5 μm. Thehorizontal and/or vertical deviation of the surface of the layer ofhardened material from planarity may be at most about 100 μm, 90 μm, 80,70 μm, 60 μm, 50 μm, 40 μm, 30 μm, 20 μm, 10 μm, or 5 μm. The horizontaland/or vertical deviation of the surface of the layer of hardenedmaterial from planarity may be any value between the afore-mentionedheight deviation values (e.g., from about 100 μm to about 5 μm, fromabout 50 μm to about 5 μm, from about 30 μm to about 5 μm, or from about20 μm to about 5 μm). The height uniformity may comprise high precisionuniformity. The resolution of the 3D object may be at least about 100dots per inch (dpi), 300 dpi, 600 dpi, 1200 dpi, 2400 dpi, 3600 dpi, or4800 dpi. The resolution of the 3D object may be any value between theafore-mentioned values (e.g., from 100 dpi to 4800 dpi, from 300 dpi to2400 dpi, or from 600 dpi to 4800 dpi). A dot may be a melt pool. A dotmay be a step (e.g., layer height). A dot may be a height of the layerof hardened material. A step may have a value of at most the height ofthe layer of hardened material. The vertical (e.g., height) uniformityof a layer of hardened material may persist across a portion of thelayer surface that has a FLS (e.g., a width and/or a length) of at leastabout 1 mm, 2 mm, 3 mm, 4 mm, 5 mm, or 10 mm; and have a heightdeviation of at least about 10 mm, 9 mm, 8 mm, 7 mm, 6 mm, 5 mm, 4 mm, 3mm, 2 mm, 1 mm, 500 μm, 400 μm, 300 μm, 200 μm, 100 μm, 90 μm, 80 μm, 70μm, 60 μm, 50 μm, 40 μm, 30 μm, 20 μm, or 10 μm. The height uniformityof a layer of hardened material may persist across a portion of thetarget surface that has a FLS (e.g., a width and/or a length) of anyvalue between the afore-mentioned width and/or length values (e.g., fromabout 10 mm to about 10 μm, from about 10 mm to about 100 μm, or fromabout 5 mm to about 500 μm). The target surface may be a layer ofhardened material (e.g., as part of the 3D object).

Characteristics of the 3D object (e.g., hardened material) and/or any ofits parts (e.g., layer of hardened material) can be measured by any ofthe following measurement methodologies. For example, the FLS values(e.g., of the width, height uniformity, auxiliary support space, and/orradius of curvature) of the layer of the 3D object and any of itscomponents (e.g., layer of hardened material) may be measured by any ofthe following measuring methodologies. The measurement methodologies maycomprise a microscopy method (e.g., any microscopy method describedherein). The measurement methodologies may comprise a coordinatemeasuring machine (CMM), measuring projector, vision measuring system,and/or a gauge. The gauge can be a gauge distometer (e.g., caliber). Thegauge can be a go-no-go gauge. The measurement methodologies maycomprise a caliber (e.g., vernier caliber), positive lens,interferometer, or laser (e.g., tracker). The measurement methodologiesmay comprise a contact or by a non-contact method. The measurementmethodologies may comprise one or more sensors (e.g., optical sensorsand/or metrological sensors). The measurement methodologies may comprisea metrological measurement device (e.g., using metrological sensor(s)).The measurements may comprise a motor encoder (e.g., rotary and/orlinear). The measurement methodologies may comprise using anelectromagnetic beam (e.g., visible or IR). The microscopy method maycomprise ultrasound or nuclear magnetic resonance. The microscopy methodmay comprise optical microscopy. The microscopy method may compriseelectromagnetic, electron, or proximal probe microscopy. The electronmicroscopy may comprise scanning, tunneling, X-ray photo-, or Augerelectron microscopy. The electromagnetic microscopy may compriseconfocal, stereoscope, or compound microscopy. The microscopy method maycomprise an inverted or non-inverted microscope. The proximal probemicroscopy may comprise atomic force, scanning tunneling microscopy, orany other microscopy method. The microscopy measurements may compriseusing an image analysis system. The measurements may be conducted atambient temperatures (e.g., R.T.), melting point temperature (e.g., ofthe pre-transformed material) or cryogenic temperatures.

The microstructures (e.g., of melt pools) of the 3D object may bemeasured by a microscopy method (e.g., any microscopy method describedherein). The microstructures may be measured by a contact or by anon-contact method. The microstructures may be measured by using anelectromagnetic beam (e.g., visible or IR). The microstructuremeasurements may comprise evaluating the dendritic arm spacing and/orthe secondary dendritic arm spacing (e.g., using microscopy). Themicroscopy measurements may comprise an image analysis system. Themeasurements may be conducted at ambient temperatures (e.g., R.T.),melting point temperature (e.g., of the pre-transformed material), orcryogenic temperatures.

Various distances relating to the chamber can be measured using any ofthe measurement techniques. For example, the gap distance (e.g., fromthe cooling member to the exposed surface of the material bed) may bemeasured using any of the measurement techniques. For example, themeasurements techniques may comprise interferometry and/or confocalchromatic measurements. The measurements techniques may comprise atleast one motor encoder (rotary, linear). The measurement techniques maycomprise one or more sensors (e.g., optical sensors and/or metrologicalsensors). The measurement techniques may comprise at least one inductivesensor. The measurement techniques may include an electromagnetic beam(e.g., visible or IR). The measurements may be conducted at ambienttemperatures (e.g., R.T.), melting point temperature (e.g., of thepre-transformed material) or cryogenic temperatures.

In some embodiments, the methods described herein provide surfaceuniformity across the exposed surface of the material bed (e.g., top ofa powder bed). For example, the surface uniformity may be such thatportions of the exposed surface that comprises the dispensed material,which are separated from one another by a distance of from about 1 mm toabout 10 mm, have a vertical (e.g., height) deviation from about 100 μmto about 5 μm. The methods described herein may achieve a deviation froma planar uniformity of the layer of pre-transformed material (e.g.,powder) in at least one plane (e.g., horizontal plane) of at most about20%, 10%, 5%, 2%, 1% or 0.5%, as compared to the average or mean plane(e.g., horizontal plane) created (e.g., formed) at the exposed surfaceof the material bed (e.g., top of a powder bed) and/or as compared tothe platform (e.g., building platform). The vertical deviation can bemeasured by using one or more sensors (e.g., optical sensors).

The 3D object can have various surface roughness profiles, which may besuitable for various applications. In some examples, the surfaceroughness is the deviations in the direction of the normal vector of areal surface (e.g., average or mean planarity of an exposed surface ofthe 3D object), from its ideal form. The surface may be the exposed topor bottom surface of a layer of hardened material. The surface may bethe exposed top or bottom surface of a ledge of hardened material. Theledge may be (e.g., substantially) planar, or comprising an angle withrespect to the platform (e.g., a rising or declining ledge). The surfaceroughness may be measured as the arithmetic average of the roughnessprofile (hereinafter “Ra”). The 3D object can have a Ra value of atleast about 300 μm, 200 μm, 100 μm, 75 μm, 50 μm, 45 μm, 40 μm, 35 μm,30 μm, 25 μm, 20 μm, 15 μm, 10 μm, 7 μm, 5 μm, 3 μm, 1 μm, 500 nm, 400nm, 300 nm, 200 nm, 100 nm, 50 nm, 40 nm, or 30 nm. The formed objectcan have a Ra value of at most about 300 μm, 200 μm, 100 μm, 75 μm, 50μm, 45 μm, 40 μm, 35 μm, 30 μm, 25 μm, 20 μm, 15 μm, 10 μm, 7 μm, 5 μm,3 μm, 1 μm, 500 nm, 400 nm, 300 nm, 200 nm, 100 nm, 50 nm, 40 nm, or 30nm. The 3D object can have a Ra value between any of the afore-mentionedRa values (e.g., from about 300 μm to about 50 μm, from about 50 μm toabout 5 μm, from about 5 μm to about 300 nm, from about 300 nm to about30 nm, or from about 300 μm to about 30 nm). The Ra values may bemeasured by a roughness tester and/or by a microscopy method (e.g., anymicroscopy method described herein). The measurements may be conductedat ambient temperatures (e.g., R.T.), melting point temperature (e.g.,of the pre-transformed material) or cryogenic temperatures. Theroughness (e.g., Ra value) may be measured by a contact or by anon-contact method. The roughness measurement may comprise one or moresensors (e.g., optical sensors). The roughness measurement may compriseusing a metrological measurement device (e.g., using metrologicalsensor(s)). The roughness may be measured using an electromagnetic beam(e.g., visible or IR).

The 3D object may be composed of successive layers of solid materialthat originated from a transformed material (e.g., that subsequentlyhardened). The successive layers of solid material may correspond tosuccessive cross sections of a desired 3D object (e.g., virtual slices).The transformed material may connect (e.g., weld) to a hardened (e.g.,solidified) material. The hardened material may reside within the samelayer as the transformed material, or in another layer (e.g., a previouslayer). In some examples, the hardened material comprises disconnectedparts of the 3D object, that are subsequently connected by newlytransformed material (e.g., in a subsequently formed layer).Transforming may comprise fusing, binding or otherwise connecting thepre-transformed material (e.g., connecting the particulate material).Fusing may comprise sintering or melting.

A cross section (e.g., vertical cross section) of the generated (i.e.,formed) 3D object may reveal a microstructure or a grain structureindicative of a layered deposition. Without wishing to be bound totheory, the microstructure or grain structure may arise due to thesolidification of transformed (e.g., powder) material that is typical toand/or indicative of the 3D printing method. For example, a crosssection may reveal a microstructure resembling ripples or waves that areindicative of (e.g., successive) solidified melt pools that may beformed during the 3D printing process. FIGS. 10A and 10B show examplesof successive melt pool in a 3D object that are arranged in rows (e.g.,layers).

The repetitive layered structure of the solidified melt pools relativeto an external plane of the 3D object may reveal the orientation atwhich the part was printed, as the deposition of the melt pools is in asubstantially horizontal plane. FIG. 10C shows examples of 3D objectsthat are formed by layerwise deposition, which layer orientation withrespect to an external plane of the 3D object reveals the orientation ofthe object during its 3D printing. For example, a 3D object having anexternal plane 1001 was formed in a manner that both the external plane1001 and the layers of hardened material (e.g., 1005) were formedsubstantially parallel to the platform 1003. For example, a 3D objecthaving an external plane 1002 was formed in a way that the externalplane 1002 formed an angle with the platform 1003, whereas the layers ofhardened material (e.g., 1006) were formed substantially parallel to theplatform 1003 (e.g., in accordance with a layerwise depositiontechnique). The 3D object having an external plane 1004 shows an exampleof a 3D object that was generated such that its external plane 1004formed an angle (e.g., alpha) with the platform 1003; which printed 3Dobject was placed on the platform 1003 after its generation was complete(e.g., in its natural orientation); wherein during its generation (e.g.,build), the layers of hardened material (e.g., 1007) were orientedsubstantially parallel to the platform 1003. The natural orientation isan orientation in which the 3D object would be expected to reside induring everyday use. FIGS. 10A and 10B show 3D objects comprising layersof solidified melt pools that are arranged in layers having layeringplanes (e.g., 1020).

In some embodiments, the (e.g., vertical and/or horizontal) crosssection of the 3D object reveals a substantially repetitivemicrostructure (or grain structure). The microstructure (or grainstructure) may comprise (e.g., substantially) repetitive variations inmaterial composition, grain orientation, material density, degree ofcompound segregation or of element segregation to grain boundaries,material phase, metallurgical phase, crystal phase, crystal structure,material porosity, or any combination thereof. The microstructure (orgrain structure) may comprise (e.g., substantially) repetitivesolidification of layered melt pools. (e.g., FIGS. 10A-10B). The (e.g.,substantially) repetitive microstructure may have an average height ofat least about 0.5 μm, 1 μm, 5 μm, 10 μm, 20 μm, 30 μm, 40 μm, 50 μm, 60μm, 70 μm, 80 μm, 90 μm, 100 μm, 150 μm, 200 μm, 250 μm, 300 μm, 350 μm,400 μm, 450 μm, 500 μm, or 1000 μm. The (e.g., substantially) repetitivemicrostructure may have an average height of at most about 1000 μm, 500μm, 450 μm, 400 μm, 350 μm, 300 μm, 250 μm, 200 μm, 150 μm, 100 μm, 90μm, 80 μm, 70 μm, 60 μm, 50 μm, 40 μm, 30 μm, 20 μm, or 10 μm. Thesubstantially repetitive microstructure may have an average height ofany value between the afore-mentioned values (e.g., from about 0.5 μm toabout 1000 μm, from about 15 μm to about 50 μm, from about 5 μm to about150 μm, from about 20 μm to about 100 μm, or from about 10 μm to about80 μm). The microstructure (e.g., melt pool) height may correspond tothe height of a layer of hardened material. The layer height can be seenin the example of FIG. 5 showing a layer of hardened material with aheight that is designated by “h|”.

In some examples, the pre-transformed material within the material bed(e.g., that was not transformed to form the 3D object) can be configuredto provide support to the 3D object. For example, the supportivepre-transformed material (e.g., powder) may be of the same type ofpre-transformed material from which the 3D object is generated, of adifferent type, or any combination thereof The pre-transformed materialmay be a particulate material (e.g., powder). The pre-transformedmaterial may be flowable during at least a portion of the 3D printing(e.g., during the entire 3D printing). The material bed may be at a(e.g., substantially) constant pressure during the 3D printing. Thematerial bed may lack a pressure gradient during the 3D printing. Thepre-transformed material within the material bed (e.g., that was nottransformed to form the 3D object) can be at an ambient temperatureduring the 3D printing. The pre-transformed material in any of thelayers in the material bed may be flowable. Before, during and/or at theend of the 3D printing process, the pre-transformed material (e.g.,powder) that did not transform to form the 3D object may be flowable.The pre-transformed material that did not transform to form the 3Dobject (or a portion thereof) may be referred to as a “remainder.” Insome instances, a low flowability pre-transformed material can becapable of supporting a 3D object better than a high flowabilitypre-transformed material. A low flowability particulate material can beachieved inter alia with a particulate material composed of relativelysmall particles, with particles of non-uniform size or with particlesthat attract each other. The pre-transformed material may be of low,medium, or high flowability. The pre-transformed material may havecompressibility of at least about 1%, 2%, 3%, 4%, 5%, 6%, 7%, 8%, 9%, or10% in response to an applied force of 15 kilo Pascals (kPa). Thepre-transformed material may have a compressibility of at most about 9%,8%, 7%, 6%, 5%, 4.5%, 4.0%, 3.5%, 3.0%, 2.5%, 2.0%, 1.5%, 1.0%, or 0.5%in response to an applied force of 15 kilo Pascals (kPa). Thepre-transformed material may have basic flow energy of at least about100 milli-Joule (mJ), 200 mJ, 300 mJ, 400 mJ, 450 mJ, 500 mJ, 550 mJ,600 mJ, 650 mJ, 700 mJ, 750 mJ, 800 mJ, or 900 mJ. The pre-transformedmaterial may have basic flow energy of at most about 200 mJ, 300 mJ, 400mJ, 450 mJ, 500 mJ, 550 mJ, 600 mJ, 650 mJ, 700 mJ, 750 mJ, 800 mJ, 900mJ, or 1000 mJ. The pre-transformed material may have basic flow energyin between the above listed values of basic flow energy values (e.g.,from about 100 mj to about 1000 mJ, from about 100 mj to about 600 mJ,or from about 500 mj to about 1000 mJ). The pre-transformed material mayhave a specific energy of at least about 1.0 milli-Joule per gram(mJ/g), 1.5 mJ/g, 2.0 mJ/g, 2.5 mJ/g, 3.0 mJ/g, 3.5 mJ/g, 4.0 mJ/g, 4.5mJ/g, or 5.0 mJ/g. The powder may have a specific energy of at most 5.0mJ/g, 4.5 mJ/g, 4.0 mJ/g, 3.5 mJ/g, 3.0 mJ/g, 2.5 mJ/g, 2.0 mJ/g, 1.5mJ/g, or 1.0 mJ/g. The pre-transformed material may have a specificenergy in between any of the above values of specific energy (e.g., fromabout 1.0 mJ/g to about 5.0 mJ/g, from about 3.0 mJ/g to about 5 mJ/g,or from about 1.0 mJ/g to about 3.5 mJ/g).

In some embodiments, during its formation (e.g., layerwise generation),the 3D object has one or more auxiliary features. In some embodiments,during its formation (e.g., layerwise generation), the 3D object isdevoid of any auxiliary features. The auxiliary feature(s) can besupported by the material (e.g., powder) bed and/or by the enclosure. Insome instances, the auxiliary supports may connect (e.g., anchor) to theenclosure (e.g., the platform). In some instances, the auxiliarysupports may not connect (e.g., not be anchored) to the enclosure (e.g.,the platform). In some instances, the auxiliary supports may not connectto the enclosure, but contact the enclosure. The 3D object comprisingone or more auxiliary supports, or devoid of auxiliary support, may besuspended (e.g., float anchorlessly) in the material bed. The floating3D object (with or without the one or more auxiliary supports) maycontact the enclosure.

The term “auxiliary feature,” or “auxiliary support” as used herein,generally refers to a feature that is part of a printed 3D object, butis not part of the desired, intended, designed, ordered, modeled,requested or final 3D object delivered to the requesting entity.Auxiliary feature(s) (e.g., auxiliary supports) may provide structuralsupport during and/or subsequent to the formation of the 3D object.Auxiliary feature(s) may enable the removal of energy from the 3D objectwhile it is being formed. Examples of an auxiliary feature comprise(heat) fin, wire, anchor, handle, support, pillar, column, frame,footing, scaffold, flange, projection, protrusion, mold (a.k.a. mould),platform (e.g., base), or any other stabilization feature. In someinstances, the auxiliary support is a scaffold that encloses the 3Dobject or part thereof. The scaffold may comprise lightly sintered orlightly fused pre-transformed (e.g.,) material. The scaffold maycomprise a continuously sintered (e.g., lightly sintered) structure thatspans at most about 1 millimeter (mm), 2 mm, 5 mm or 10 mm. The scaffoldmay comprise a continuously sintered structure that spans at least about1 millimeter (mm), 2 mm, 5 mm or 10 mm. The scaffold may comprise acontinuously sintered structure having a FLS between any of theafore-mentioned dimensions (e.g., from about 1 mm to about 10 mm, orfrom about 1 mm to about 5 mm). In some examples, the 3D object may beprinted without a supporting scaffold. The supporting scaffold mayengulf at least a portion of the 3D object (e.g., the entire 3D object).For example, a supporting scaffold that floats anchorlessly in thematerial bed, or that is connected to at least a portion of theenclosure. The supporting scaffold may comprise a dense arrangement(e.g., array) of support structures. The support(s) or support mark(s)can stem from or appear on the surface of the 3D object. The auxiliarysupports or support marks can stem from or appear on an external surfaceand/or on an internal surface (e.g., a cavity within the 3D object). The3D object can have auxiliary features that are supported by the materialbed (e.g., powder bed) and not touch the base, substrate, containeraccommodating the material bed, and/or the bottom of the enclosure. The3D part (3D object) in a complete or partially formed state, can becompletely supported by the material bed (e.g., without being anchoredto the substrate, base, container accommodating the powder bed, orotherwise to the enclosure). The 3D object in a complete or partiallyformed state can be (completely) supported by the material bed (e.g.,without touching anything except the material constituting the materialbed). The 3D object in a complete or partially formed state can besuspended anchorlessly in the material bed without resting on anyadditional support structures. In some cases, the 3D object in acomplete or partially formed state can freely float (e.g., anchorlessly)in the material bed (e.g., during at least a portion of the 3D printing(e.g., during the entire 3D printing)). Suspended may comprise floating,disconnected, anchorless, detached, non-adhered, or free. In someexamples, the 3D object may not be anchored (e.g., connected) to atleast a part of the enclosure (e.g., during formation of the 3D object,and/or during formation of at least one layer of the 3D object). Theenclosure may comprise a platform or wall that define the material bed.The 3D object may not touch and/or not contact enclosure (e.g., duringformation of at least one layer of the 3D object).

The printed 3D object may be printed without the use of auxiliaryfeatures, may be printed using a reduced number of auxiliary features,or printed using spaced apart auxiliary features. In some embodiments,the printed 3D object may be devoid of (one or more) auxiliary supportfeatures or auxiliary support feature marks that are indicative of a(e.g., prior) presence and/or removal of the auxiliary supportfeature(s). The 3D object may be devoid of one or more auxiliary supportfeatures and of one or more marks of an auxiliary feature (including abase structure) that was removed (e.g., subsequent to, orcontemporaneous with, the generation of the 3D object). The printed 3Dobject may comprise a single auxiliary support mark. The singleauxiliary feature (e.g., auxiliary support or auxiliary structure) maybe a platform (e.g., a building platform such as a base or substrate),or a mold. The auxiliary support may adhere to the platform and/or mold.The 3D object may comprise marks belonging to one or more (e.g.,previously present) auxiliary structures. The 3D object may comprise twoor more marks belonging to auxiliary feature(s). The 3D object may bedevoid of marks pertaining to at least one auxiliary support. The 3Dobject may be devoid of one or more auxiliary support. The mark maycomprise variation in grain orientation, variation in layeringorientation, layering thickness, material density, the degree ofcompound segregation to grain boundaries, material porosity, the degreeof element segregation to grain boundaries, material phase,metallurgical phase, crystal phase, crystal structure, or anycombination thereof; wherein the variation may not have been created bythe geometry of the 3D object alone, and may thus be indicative of aprior existing auxiliary support that was removed. The variation may beforced upon the generated 3D object by the geometry of the support. Insome instances, the 3D structure of the printed object may be forced bythe auxiliary support(s) (e.g., by a mold). For example, a mark may be apoint and/or area of discontinuity that is not explained by the geometryof the 3D object, which does not include any auxiliary support(s). Thepoint and/or area of discontinuity may arise form a (e.g., mechanicaland/or optical) trimming of the auxiliary support(s). FIG. 34 shows anexample of a vertical cross section of 3D object comprising twosubstantially horizontal layers (e.g., 3401 and 3402), and a verticalauxiliary support that comprises an area of discontinuity 3404 andintroduces a geometrical deformation (e.g. 3403) in layers 3401 and 3402which is caused by the presence of auxiliary support, and cannot beotherwise explained (and thus indicates its presence). A mark may be asurface feature that cannot be explained by the geometry of a 3D object,if it did not include any auxiliary support(s) (e.g., a mold). The twoor more auxiliary features or auxiliary support feature marks may bespaced apart by a spacing distance (e.g., XY) of at least 1.5millimeters (mm), 2 mm, 2.5 mm, 3 mm, 3.5 mm, 4 mm, 4.5 mm, 5 mm, 5.5mm, 6 mm, 6.5 mm, 7 mm, 7.5 mm, 8 mm, 8.5 mm, 9 mm, 9.5 mm, 10 mm, 10.5mm, 11 mm, 11.5 mm, 12 mm, 12.5 mm, 13 mm, 13.5 mm, 14 mm, 14.5 mm, 15mm, 15.5 mm, 16 mm, 20 mm, 20.5 mm, 21 mm, 25 mm, 30 mm, 30.5 mm, 31 mm,35 mm, 40 mm, 40.5 mm, 41 mm, 45 mm, 50 mm, 80 mm, 100 mm, 200 mm 300mm, or 500 mm. The two or more auxiliary support features or auxiliarysupport feature marks may be spaced apart by a spacing distance of anyvalue between the afore-mentioned auxiliary support space values (e.g.,from 1.5 mm to 500 mm, from 2 mm to 100 mm, from 15 mm to 50 mm, or from45 mm to 200 mm). This distance is collectively referred to herein asthe “auxiliary feature spacing distance.”

The 3D object may comprise an impeller such as, for example, a shrouded(e.g., covered) impeller that is produced as one piece (e.g., comprisingblades and cover) during one 3D printing process. The impeller may beused for pumps (e.g., turbo pumps). The 3D object may comprise aturbine, stator, motor, or rotor. The 3D object may comprise a blade(e.g., 3D plane) that is formed in the material bed such that at leastone blade (e.g., all blades) is substantially parallel (e.g., completelyparallel or almost parallel), or at an angle of at most about 10°, 20°,30°, 40°, 45°, or 90° with respect to the platform during the formationof the 3D object. The 3D object may comprise a blade (e.g., 3D plane)that is formed in the material bed such that the blade is at any anglebetween the afore-mentioned angles (e.g., from about 0° to about 10°,from about 0° to about 20°, from about 0° to about 30°, from about 0° toabout 40°, from about 0° to about 45°, or from about 0° to about 90°with respect to the platform) during the formation of the 3D object. The3D object may comprise a blade (e.g., 3D plane) that is formed in thematerial bed such that the blade is substantially perpendicular (e.g.,completely perpendicular or almost perpendicular) or at an angle of atmost 80°, 70°, 60°, 50°, or 0° with respect to the rotational axis ofthe 3D object (e.g., when the 3D object is an impeller, turbine, stator,motor, or rotor). The 3D object may comprise a blade (e.g., 3D plane)that is formed in the material bed such that the blade is at any anglebetween the afore-mentioned angles (e.g., from about 90° to about 80°,from about 90° to about 70°, from about 90° to about 60°, from about 90°to about 50°, from about 90° to about 0°, with respect to the rotationalaxis of the 3D object). In some examples, the hanging structure (e.g.,blade) does not comprise auxiliary support (e.g., except for therotational axis). In some examples, the hanging structure (e.g., blade)comprises at least one auxiliary support, wherein the distance betweenevery two auxiliary supports, or a distance between an auxiliary supportand the rotational axis, is of a value equating the auxiliary featurespacing distance (e.g., disclosed herein). The 3D object may comprise acomplex internal structure. The 3D object may comprise a plurality ofblades. A distance between two blades may be at most about 0.1 mm, 0.2mm, 0.5 mm, 1 mm, 2 mm, 3 mm, 4 mm, 5 mm, 6 mm, 7 mm, 8 mm, 10 mm, 20mm, 50 mm, or 100 mm. A distance between two blades may be any valuebetween the afore-mentioned values (e.g., from about 0.1 mm to about 100mm, from about 0.1 mm to about 5 mm, from about 0.1 mm to about 10 mm,from about 0.1 mm to about 50 mm, or from about 10 mm to about 100 mm).The distance between the blades may refer to a vertical distance. Thedistance between the blades may constitute an atmospheric gap.

FIG. 9 shows an example of a coordinate system. Line 904 represents avertical cross section of a layering plane. Line 903 represents the(e.g., shortest) straight line connecting the two auxiliary supports orauxiliary support marks. Line 902 represent the normal to the layeringplane. Line 901 represents the direction of the gravitational field. Theacute (i.e., sharp) angle alpha between the straight (e.g., shortest)line connecting the two auxiliary supports or auxiliary support marksand the direction of normal to the layering plane may be at least about45 degrees(°), 50°, 55°, 60°, 65°, 70°, 75°, 80°, or 85°. The acuteangle alpha between the straight line connecting the two auxiliarysupports or auxiliary support marks and the direction of normal to thelayering plane may be at most about 90°, 85°, 80°, 75°, 70°, 65°, 60°,55°, 50°, or 45°. The acute angle alpha between the straight lineconnecting the two auxiliary supports or auxiliary support marks and thedirection of normal to the layering plane may be any angle range betweenthe afore-mentioned angles (e.g., from about 45 degrees(°), to about90°, from about 60° to about 90°, from about 75° to about 90°, fromabout 80° to about 90°, or from about 85° to about 90°). FIG. 18 showsan example of a 3D object comprising successive layers of material. Eachof the layers has a (e.g., average) layering plane (e.g., 1806). Thelayering planes may be substantially parallel to each other. The 3Dobject has a top surface 1802, and is disposed above (e.g., and on) aplatform 1803. The 3D object comprises two auxiliary supports 1808. The3D object comprises an external (e.g., bottom) surface to which theauxiliary supports 1808 are connected. The shortest distance between thetwo auxiliary supports resides on line 1807. The line 1807 forms anacute angle alpha with the normal 1804 to the layering plane (e.g.,1806). The acute angle alpha between the shortest line connecting thetwo auxiliary supports (or auxiliary support marks) and the directionnormal to the layering plane may be from about 87° to about 90°. Anexample of a layering plane can be seen in FIG. 7 showing a verticalcross section of a 3D object 711 that comprises layers 1 to 6, each ofwhich are substantially planar. In the schematic example in FIG. 7, thelayering plane of the layers can be the layer. For example, layer 1could correspond to both the layer and the layering plane of layer 1.When the layer is not planar (e.g., FIG. 7, layer 5 of 3D object 712),the layering plane would be the average or mean plane of the layer. Thetwo auxiliary supports or auxiliary support feature marks can be on thesame surface (e.g., external surface of the 3D object). The same surfacecan be an external surface or an internal surface (e.g., a surface of acavity within the 3D object). When the angle between the shorteststraight line connecting the two auxiliary supports or auxiliary supportmarks and the direction of normal to the layering plane is greater than90 degrees, one can consider the complementary acute angle. In someembodiments, any two auxiliary supports or auxiliary support marks arespaced apart by at least about 10.5 millimeters or more. In someembodiments, any two auxiliary supports or auxiliary support marks arespaced apart by at least about 40.5 millimeters or more. In someembodiments, any two auxiliary supports or auxiliary support marks arespaced apart by the auxiliary feature spacing distance

In some embodiments, the one or more auxiliary features (which mayinclude a base support) are used to hold and/or restrain the 3Dobjectduring formation of the 3D object. Such restraint may preventdeformation of the 3D object during its formation and/or during its(e.g., complete) hardening. In some cases, auxiliary features can beused to anchor and/or hold a 3D object or a portion of a 3D object in amaterial bed (e.g., with or without contacting the enclosure, and/orwith or without connecting to the enclosure). The one or more auxiliaryfeatures can be specific to a 3D object and can increase the time,energy, material and/or cost required to form the 3D object. The one ormore auxiliary features can be removed prior to use or delivery (e.g.,distribution) of the 3D object. The longest dimension of a (e.g.,horizontal) cross-section of an auxiliary feature can be at most about50 nm, 100 nm, 200 nm, 300 nm, 400 nm, 500 nm, 600 nm, 700 nm, 800 nm,900 nm, or 1000 nm, 1 μm, 3 μm, 10 μm, 20 μm, 30 μm, 100 μm, 200 μm, 300μm, 400 μm, 500 μm, 700 μm, 1 mm, 3 mm, 5 mm, 10 mm, 20 mm, 30 mm, 50mm, 100 mm, or 300 mm. The longest dimension (e.g., FLS) of a (e.g.,horizontal) cross-section of an auxiliary feature can be at least about50 nm, 100 nm, 200 nm, 300 nm, 400 nm, 500 nm, 600 nm, 700 nm, 800 nm,900 nm, or 1000 nm, 1 μm, 3 μm, 10 μm, 20 μm, 30 μm, 100 μm, 200 μm, 300μm, 400 μm, 500 μm, 700 μm, 1 mm, 3 mm, 5 mm, 10 mm, 20 mm, 30 mm, 50mm, 100 mm, or 300 mm. The longest dimension of a (e.g., horizontal)cross-section of an auxiliary feature can be any value between theabove-mentioned values (e.g., from about 50 nm to about 300 mm, fromabout 5 μm to about 10 mm, from about 50 nm to about 10 mm, or fromabout 5 mm to about 300 mm). Eliminating the need for auxiliary featurescan decrease the time, energy, material, and/or cost associated withgenerating the 3D object (e.g., 3D part). In some examples, the 3Dobject may be formed with auxiliary features. In some examples, the 3Dobject may be formed while connecting to the container that accommodatesthe material bed (e.g., side(s) and/or bottom of the container).

In some examples, the diminished number of auxiliary supports or lack ofone or more auxiliary supports, will provide a 3D printing process thatrequires a smaller amount of material, energy, material, and/or cost ascompared to commercially available 3D printing processes. In someexamples, the diminished number of auxiliary supports or lack of one ormore auxiliary supports, will provide a 3D printing process thatproduces a smaller amount of material waste as compared to commerciallyavailable 3D printing processes. The smaller amount can be smaller by atleast about 1.1, 1.3, 1.5, 2, 3, 4, 5, 6, 7, 8, 9, or 10. The smalleramount may be smaller by any value between the aforesaid values (e.g.,from about 1.1 to about 10, or from about 1.5 to about 5).

At least a portion of the 3D object can be vertically displaced (e.g.,sink) in the material bed during the 3D printing. During the 3Dprinting: At least a portion of the 3D object can be surrounded bypre-transformed material within the material bed (e.g., submerged). Atleast a portion of the 3D object can rest in the pre-transformedmaterial without (e.g., substantial) vertical movement (e.g.,displacement). Lack of (e.g., substantial) vertical displacement canamount to a vertical movement (e.g., sinking) of at most about 40%, 20%,10%, 5%, or 1% of the layer thickness. Lack of (e.g., substantial)sinking can amount to at most about 100 μm, 30 μm, 10 μm, 3 μm, or 1 μm.Substantial may be relative to the effect on the 3D printing process.Lack of substantial sinking and/or vertical movement may refer to anegligible effect of the sinking and/or vertical movement on the 3Dprinting. At least a portion of the 3D object can rest in thepre-transformed material without substantial movement (e.g., horizontal,vertical, and/or angular). Lack of substantial movement can amount to amovement of at most 100 μm, 30 μm, 10 μm, 3 μm, or 1 μm. The 3D objectcan rest above (e.g., on) the platform (e.g., substrate) when the 3Dobject is vertically displaced (e.g., sunk) or submerged in the materialbed.

FIG. 1 depicts an example of a system that can be used to generate a 3Dobject using a 3D printing process disclosed herein (e.g., a 3Dprinter). The system can include an enclosure (e.g., a chambercomprising a wall 107). At least a fraction of the components in thesystem (e.g., components of the 3D printer) can be enclosed in thechamber. At least a fraction of the chamber can be filled with a gas tocreate a gaseous environment (i.e., an atmosphere 126). The gas can bean inert gas (e.g., Argon, Neon, Helium, Nitrogen). The chamber can befilled with at least one other gas (e.g., a mixture of gases). The gascan be a non-reactive gas (e.g., an inert gas). The gaseous environmentcan comprise argon, nitrogen, helium, neon, krypton, xenon, hydrogen,carbon monoxide, or carbon dioxide. At times, the (gas) composition ofthe atmosphere may vary be controlled. The control may be before,during, and/or after the 3D printing. The control may be automatically(e.g., using a controller) or manual. During the 3D printing, maycomprise before, after, and/or during the irradiation of the targetsurface by the energy beam. Varying the atmosphere may comprise reducingthe oxygen and/or water content. Varying the atmosphere may compriseintroducing a reactive agent (e.g., hydrogen). The reactive agent may bea reducing agent. The reactive agent may react with oxygen and/or waterin the atmosphere to reduce its concentration therein. The agent may bean absorbing agent (e.g., or oxygen and/or water). The 3D printer maycomprise a cryogenic apparatus (e.g., cryogenic finger) that may reducethe content of hydrogen and/or oxygen from the atmosphere (e.g., onwhich water and/or oxygen can condense and/or crystalize). For example,the atmosphere may comprise a forming gas. The (volume per volume)percentage of reducing agent (e.g., hydrogen) in the atmosphere may beat most about 10%, 8%, 5%, 2%, 1%, 0.5%, 0.1%, or 0.05%. The (volume pervolume) percentage of reducing agent in the atmosphere may be of anyvalue between the afore-mentioned values (e.g., from about 10% to about0.1%, from about 2% to about 0.1%, or from about 5%, to about 0.05%). Insome embodiments, the processing chamber may be pressurized aboveambient atmospheric pressure. The pressure in the chamber can be atleast about 10⁻⁷ Torr, 10⁻⁶ Torr, 10⁻⁵ Torr, 10⁻⁴ Torr, 10⁻³ Torr, 10⁻²Torr, 10⁻¹ Torr, 1 Torr, 10 Torr, 100 Torr, 1 bar, 2 bar, 3 bar, 4 bar,5 bar, 10 bar, 20 bar, 30 bar, 40 bar, 50 bar, 100 bar, 200 bar, 300bar, 400 bar, 500 bar, or 1000 bar. The pressure in the chamber can beat least about 100 Torr, 200 Torr, 300 Torr, 400 Torr, 500 Torr, 600Torr, 700 Torr, 720 Torr, 740 Torr, 750 Torr, 760 Torr, 900 Torr, 1000Torr, 1100 Torr, or 1200 Torr. The pressure in the chamber can be atmost about 10⁻⁸ Torr, 10⁻⁷ Torr, 10⁻⁶ Torr, 10⁻⁵ Torr, or 10⁻⁴ Torr,10⁻³ Torr, 10⁻² Torr, 10^('1) Torr, 1 Torr, 10 Torr, 100 Torr, 200 Torr,300 Torr, 400 Torr, 500 Torr, 600 Torr, 700 Torr, 720 Torr, 740 Torr,750 Torr, 760 Torr, 900 Torr, 1000 Torr, 1100 Torr, or 1200 Torr. Thepressure in the chamber can be of any value at a range between any ofthe afore-mentioned pressure values (e.g., from about 10⁻⁷ Torr to about1200 Torr, from about 10⁻⁷ Torr to about 1 Torr, from about 1 Torr toabout 1200 Torr, from about 10⁻² Torr to about 10 Torr, from about 10⁻⁷Torr to about 10 bar, from about 10⁻⁷ Torr to about 1 bar, or from about1 bar to about 10 bar). The pressure can be measured by a pressuregauge. The pressure can be measured at ambient temperature (e.g., R.T.),cryogenic temperature, or at the temperature of the melting point of thepre-transformed material. In some cases, the pressure in the chamber canbe standard atmospheric pressure. In some cases, the pressure in thechamber can be ambient pressure (e.g., neutral pressure). In someexamples, the chamber can be under vacuum pressure. In some examples,the chamber can be under a positive pressure (e.g., above ambientpressure). The pressure may be ambient pressure during the 3D printingprocess. The chamber pressures mentioned herein may be during at least aportion of the 3D printing. In some examples, the enclosure and/or anyportion thereof (e.g., the material bed) may be at a (e.g.,substantially) constant pressure value during the 3D printing process.In some embodiments, the enclosure and/or any portion thereof (e.g., thematerial bed) may be at a non-varied (e.g., non-gradual) pressure duringthe 3D printing process. The ambient pressure may be standardatmospheric pressure. The enclosure and/or any portion thereof (e.g.,material bed) may experience (e.g., substantial) homogenous pressuredistribution throughout the enclosure during at least a portion of the(e.g., the entire) 3D printing process. The chamber can comprise two ormore gaseous layers as disclosed, for example, in Provisional PatentApplication Ser. No. 62/444,069 which is incorporated herein in itsentirety. In some embodiments, the pre-transformed material ispre-treated to remove oxygen and/or water. The pre-transformed materialmay be kept in a (e.g., substantially) dry and/or oxygen freeenvironment during at least one 3D printing cycle.

The gaseous environment can comprise a gas selected from the groupconsisting of argon, nitrogen, helium, neon, krypton, xenon, hydrogen,carbon monoxide, carbon dioxide, and oxygen. The gaseous environment cancomprise air. The gas can be an ultrahigh purity gas. The ultrahighpurity gas can be at least about 99%, 99.9%, 99.99%, or 99.999% pure.The gas may comprise less than about 2 ppm oxygen, less than about 3 ppmmoisture, less than about 1 ppm hydrocarbons, or less than about 6 ppmnitrogen. In some embodiments, the pre-transformed material (e.g., inthe material bed) may be degassed before the 3D printing initiates(e.g., before its first irradiation by the transforming energy beam).The enclosure can be maintained under vacuum or under an inert, dry,non-reactive and/or oxygen reduced (or otherwise controlled) atmosphere.In some examples, the enclosure is under vacuum. The atmosphere can befurnished by providing an inert, dry, non-reactive, and/or oxygenreduced gas (e.g., Ar). The atmosphere can be furnished by flowing thegas through the enclosure (e.g., chamber).

The material layer can be supported on a platform. The platform maycomprise a substrate (e.g., 109). The substrate can have a circular,rectangular, square, or irregularly shaped cross-section. The platformmay comprise a base (e.g., 102) disposed above the substrate. Theplatform may comprise a base (e.g., 102) disposed between the substrateand a material layer (or a space to be occupied by a material layer).One or more material-bed-seals (e.g., 103) may prevent leakage of thematerial from the material bed (e.g., 104). A thermal control unit(e.g., a cooling member such as a heat sink or a cooling plate, or aheating plate 113) can be provided inside of the region where the 3Dobject is formed or adjacent to (e.g., above) the region where the 3Dobject is formed. The thermal control unit may comprise a thermostat.Additionally, or alternatively, the thermal control unit can be providedoutside of the region where the 3D object is formed (e.g., at apredetermined distance). In some cases, the thermal control unit canform at least one section of a boundary region where the 3D object isformed (e.g., the container accommodating the material bed). Examples ofthermal control unit (e.g., cooling member) can be found in PatentApplication Serial Number PCT/US15/36802 which is incorporated herein byreference in its entirety.

In some embodiments, one or more of the 3D printer components arecontained in the enclosure (e.g., chamber). The enclosure can include areaction space that is suitable for introducing precursor to form a 3Dobject, such as pre-transformed (e.g., powder) material. The enclosurecan be a vacuum chamber, a positive pressure chamber, or an ambientpressure chamber. The enclosure can comprise a gaseous environment witha controlled pressure, temperature, and/or gas composition. The controlmay be before, during, and/or after the 3D printing. The control may beautomatic and/or manual.

In some embodiments, the concentration of oxygen and/or humidity in theenclosure (e.g., chamber) is minimized (e.g., below a predeterminedthreshold value). The gas composition of the chamber may contain a levelof oxygen and/or humidity that is at most about 100 parts per billion(ppb), 10 ppb, 1 ppb, 0.1 ppb, 0.01 ppb, 0.001 ppb, 100 parts permillion (ppm), 10 ppm, 1 ppm, 0.1 ppm, 0.01 ppm, or 0.001 ppm. The gascomposition of the chamber can contain an oxygen and/or humidity levelbetween any of the afore-mentioned values (e.g., from about 100 ppb toabout 0.001 ppm, from about 1 ppb to about 0.01 ppm, or from about 1 ppmto about 0.1 ppm). The gas composition in the environment in theenclosure can comprise a (e.g., substantially) oxygen free environment.Substantially may be relative to the effect of oxygen on the 3Dprinting, wherein substantially free may refer to a negligible effect onthe 3D printing. For example, the gas composition can contain at mostabout 100,000 parts per million (ppm), 10,000 ppm, 1000 ppm, 500 ppm,400 ppm, 300 ppm, 200 ppm, 100 ppm, 50 ppm, 30 ppm, 10 ppm, 5 ppm, 1ppm, 100,000 parts per billion (ppb), or 10,000 ppb of oxygen. The gascomposition in the environment contained within the enclosure cancomprise a substantially moisture (e.g., water) free environment. Thegaseous environment can comprise at most about 100,000 ppm, 10,000 ppm,1000 ppm, 500 ppm, 400 ppm, 300 ppm, 200 ppm, 100 ppm, 50 ppm, 30 ppm,10 ppm, 5 ppm, 1 ppm, 100,000 ppb, or 10,000 ppb of water.

The gas composition may be measures by one or more sensors (e.g., anoxygen and/or humidity sensor), before, during, and/or after the 3Dprinting. The chamber can be opened at the completion of a formation ofa 3D object. When the chamber is opened, ambient air containing oxygenand/or humidity can enter the chamber. In some embodiments, theprocessing chamber is accessed through a load lock mechanism thatreduces the contamination of the processing chamber (comprisingatmosphere 126) with the ambient atmosphere (e.g., containing oxygenand/or humidity). Exposure of one or more components in the chamber toambient atmosphere (e.g., air) can be reduced by, for example, flowingan inert gas while the chamber is open (e.g., to prevent entry ofambient air), or by flowing a heavy gas (e.g., argon) that rests on thesurface of the target surface (e.g., the exposed surface of the materialbed). In some cases, components that absorb oxygen and/or humidity on totheir surface(s) can be sealed while the enclosure (e.g., chamber) isopen (e.g., to the ambient environment).

In some embodiments, the chamber is configured such that gas inside thechamber (e.g. 126) has a relatively low leak rate from the chamber to anenvironment outside of the chamber. In some cases, the leak rate can beat most about 100 milliTorr/minute (mTorr/min), 50 mTorr/min, 25mTorr/min, 15 mTorr/min, 10 mTorr/min, 5 mTorr/min, 1 mTorr/min, 0.5mTorr/min, 0.1 mTorr/min, 0.05 mTorr/min, 0.01 mTorr/min, 0.005mTorr/min, 0.001 mTorr/min, 0.0005 mTorr/min, or 0.0001 mTorr/min. Theleak rate may be between any of the afore-mentioned leak rates (e.g.,from about 0.0001 mTorr/min to about, 100 mTorr/min, from about 1mTorr/min to about, 100 mTorr/min, or from about 1 mTorr/min to about,100 mTorr/min). The leak rate may be measured by one or more pressuregauges and/or sensors (e.g., at ambient temperature) before, during,and/or after the 3D printing. The enclosure can be sealed (e.g., usingat least one gas-seal) such that the leak rate of the gas from insidethe chamber to the environment outside of the chamber is low (e.g.,below a threshold level). The gas-seal can comprise an O-ring, rubberseal, metal seal, load-lock, or bellow on a piston. In some cases, thechamber can have a controller configured to detect leaks above aspecified leak rate (e.g., by using at least one sensor) before, during,and/or after the 3D printing. The detection may be using at least onesensor. The sensor may be operatively coupled to the controller. In someinstances, the controller can identify and/or control (e.g., directand/or regulate) the gas-leak. For example, the controller may be ableto identify a gas-leak by detecting a decrease in pressure in side ofthe chamber over a given time interval. The controller may furthernotify (e.g., a user and/or software) of the detected leak and/orperform an emergency shut-off of the 3D printer.

In some embodiments, the system and/or apparatus components describedherein are adapted and/or configured to generate a 3D object. The 3Dobject can be generated through a 3D printing process. A first layer ofpre-transformed material (e.g., powder) can be provided adjacent to aplatform. A platform (e.g., base) can be a previously formed layer ofthe 3D object or any other surface above (e.g., on) which a layer ormaterial bed comprising the pre-transformed material is spread, held,placed, adhered, attached, or supported. When the first layer of the 3Dobject is generated, this first material layer can be formed in thematerial bed without a platform (e.g., base), without one or moreauxiliary support features (e.g., rods), and/or without other supportingstructure other than the pre-transformed material (e.g., within thematerial bed). Subsequent layers or hardened material can be formed suchthat at least one portion of the subsequent layer fused (e.g., melts orsinters), binds and/or otherwise connects to the at least a portion of apreviously formed layer of hardened material (or portion thereof). Theat least a portion of the previously formed layer of hardened material(e.g., a complete layer of hardened material) can act as a platform(e.g., base) for formation of the (e.g., rest of the) 3D object. In somecases, the first formed layer of hardened material comprises and/orforms at least a portion of the platform (e.g., base). This platform maybe a sacrificial layer or form the bottom skin layer of the 3D object.The pre-transformed material layer can comprise particles of homogeneousor heterogeneous size and/or shape. The first formed layer of hardenedmaterial may float anchorlessly in the material bed during its formationand/or during the formation of the 3D object. The first formed layer ofhardened material may or may not be planar.

In some embodiments, the system, methods, and/or apparatus describedherein may comprise at least one energy source (e.g., the transformingenergy source generating the transforming energy beam, and/or thesensing energy source generating the sensing energy beam). Thetransforming energy beam may be any energy beam (e.g., scanning energybeam or tiling energy beam) disclosed in patent application No.62/265,817, and patent application No. 62/317,070 which are incorporatedherein by reference in their entirety (in those applications the tilingenergy beam may be referred to as the “(tiling) energy flux”). Theenergy source may be any energy source disclosed in patent applicationNos. 62/265,817, or in 62/317,070 which are incorporated herein byreference in their entirety. The energy beam may travel (e.g., scan)along a path. The path may be predetermined (e.g., by the controller).The methods, systems and/or apparatuses may comprise at least a secondenergy source. The second energy source may generate a second energy(e.g., second energy beam). The first and/or second energy beams (e.g ,scanning and/or tiling energy beams) may transform at least a portion ofthe pre-transformed material in the material bed to a transformedmaterial. In some embodiments, the first and/or second energy source mayheat but not transform at least a portion of the pre-transformedmaterial in the material bed. In some cases, the system can comprise 1,2, 3, 4, 5, 6, 7, 8, 9, 10, 30, 100, 300, 1000 or more energy beamsand/or sources. The system can comprise an array of energy sources(e.g., laser diode array). Alternatively, or additionally the surface,material bed, 3D object (or part thereof), or any combination thereofmay be heated by a heating mechanism. The heating mechanism may comprisedispersed energy beams. In some cases, the at least one energy source isa single (e.g., first) energy source.

In some embodiments, the energy source is a source configured to deliverenergy to a target area (e.g., a confined area). An energy source candeliver energy (e.g., radiation, e.g., beam) to the confined areathrough radiative heat transfer. The energy source can project energy(e.g., heat energy). The generated energy (e.g., beam) can interact withat least a portion of the material in the material bed. The energy canheat the material in the material bed before, during and/or after thepre-transformed (e.g., powder) material is being transformed (e.g.,melted). The energy can heat (e.g., and not transform) at least afraction of a 3D object at any point during formation of the 3D object.Alternatively or additionally, the material bed may be heated by aheating mechanism projecting energy (e.g., using radiative heat and/orenergy beam). The energy may include an energy beam and/or dispersedenergy (e.g., radiator or lamp). The energy may include radiative heat.The radiative heat may be projected by a dispersive energy source (e.g.,a heating mechanism) comprising a lamp, a strip heater (e.g., mica stripheater, or any combination thereof), a heating rod (e.g., quartz rod),or a radiator (e.g., a panel radiator). The heating mechanism maycomprise an inductance heater. The heating mechanism may comprise aresistor (e.g., variable resistor). The resistor may comprise a varistoror rheostat. A multiplicity of resistors may be configured in series,parallel, or any combination thereof. In some cases, the system can havea single (e.g., first) energy source that is used to transform at leasta portion of the material bed.

In some embodiments, the energy beam includes a radiation comprising anelectromagnetic, or charged particle beam. The energy beam may includeradiation comprising electromagnetic, electron, positron, proton,plasma, radical or ionic radiation. The electromagnetic beam maycomprise microwave, infrared, ultraviolet, or visible radiation. Theenergy beam may include an electromagnetic energy beam, electron beam,particle beam, or ion beam. An ion beam may include a cation or ananion. A particle beam may include radicals. The electromagnetic beammay comprise a laser beam. The energy beam may comprise plasma. Theenergy source may include a laser source. The energy source may includean electron gun. The energy source may include an energy source capableof delivering energy to a point or to an area (e.g., confined area). Insome embodiments, the energy source can be a laser source. The lasersource may comprise a CO₂, Nd:YAG, Neodymium (e.g., neodymium-glass), anYtterbium, or an excimer laser. The laser may comprise a fiber laser.The energy source may include an energy source capable of deliveringenergy to a point or to an area. The energy source (e.g., transformingenergy source) can provide an energy beam having an energy density of atleast about 50 joules/cm² (J/cm²), 100 J/cm², 200 J/cm², 300 J/cm², 400J/cm², 500 J/cm², 600 J/cm², 700 J/cm², 800 J/cm², 1000 J/cm², 1500J/cm², 2000 J/cm², 2500 J/cm², 3000 J/cm², 3500 J/cm², 4000 J/cm², 4500J/cm², or 5000 J/cm². The energy source can provide an energy beamhaving an energy density of at most about 50 J/cm², 100 J/cm², 200J/cm², 300 J/cm², 400 J/cm², 500 J/cm², 600 J/cm², 700 J/cm², 800 J/cm²,1000 J/cm², 500 J/cm², 1000 J/cm², 1500 J/cm², 2000 J/cm², 2500 J/cm²,3000 J/cm², 3500 J/cm², 4000 J/cm², 4500 J/cm², or 5000 J/cm². Theenergy source can provide an energy beam having an energy density of avalue between the afore-mentioned values (e.g., from about 50 J/cm² toabout 5000 J/cm², from about 200 J/cm² to about 1500 J/cm², from about1500 J/cm² to about 2500 J/cm², from about 100 J/cm² to about 3000J/cm², or from about 2500 J/cm²to about 5000 J/cm²). In an example, alaser can provide light energy at a peak wavelength of at least about100 nanometer (nm), 500 nm, 750 nm, 1000 nm, 1010 nm, 1020 nm, 1030 nm,1040 nm, 1050 nm, 1060 nm, 1070 nm, 1080 nm, 1090 nm, 1100 nm, 1200 nm,1500 nm, 1600 nm, 1700 nm, 1800 nm, 1900 nm, or 2000 nm. In an example alaser can provide light energy at a peak wavelength of at most about2000 nm, 1900 nm, 1800 nm, 1700 nm, 1600 nm, 1500 nm, 1200 nm, 1100 nm,1090 nm, 1080 nm, 1070 nm, 1060 nm, 1050 nm, 1040 nm, 1030 nm, 1020 nm,1010 nm, 1000 nm, 750 nm, 500 nm, or 100 nm. The laser can provide lightenergy at a peak wavelength between any of the afore-mentioned peakwavelength values (e.g., from about 100 nm to about 2000 nm, from about500 nm to about 1500 nm, or from about 1000 nm to about 1100 nm). Theenergy source (e.g., laser) may have a power of at least about 0.5 Watt(W), 1 W, 2 W, 3 W, 4 W, 5 W, 10 W, 20 W, 30 W, 40 W, 50 W, 60 W, 70 W,80 W, 90 W, 100 W, 120 W, 150 W, 200 W, 250 W, 300 W, 350 W, 400 W, 500W, 750 W, 800 W, 900 W, 1000 W, 1500 W, 2000 W, 3000 W, or 4000 W. Theenergy source may have a power of at most about 0.5 W, 1 W, 2 W, 3 W, 4W, 5 W, 10 W, 20 W, 30 W, 40 W, 50 W, 60 W, 70 W, 80 W, 90 W, 100 W, 120W, 150 W, 200 W, 250 W, 300 W, 350 W, 400 W, 500 W, 750 W, 800 W, 900 W,1000 W, 1500, 2000 W, 3000 W, or 4000 W. The energy source may have apower between any of the afore-mentioned laser power values (e.g., fromabout 0.5 W to about 100 W, from about 1 W to about 10 W, from about 100W to about 1000 W, or from about 1000 W to about 4000 W). The firstenergy source (e.g., producing the transforming energy beam) may have atleast one of the characteristics of the second energy source. The firstenergy source (e.g., producing the transforming energy beam) may differin at least one of the characteristics from the second energy source.

An energy beam generated by the energy source can be incident on, or bedirected perpendicular to, the target surface. The target surface maycomprise an exposed surface of the material bed or an exposed surface ofa hardened material. The hardened material may be a 3D object or aportion thereof The energy beam can be directed at an acute angle withina value ranging from being parallel to being perpendicular with respectto the average or mean plane of the target surface and/or the platform.The energy beam can be directed onto a specified area of at least aportion of the target surface for a specified time-period (e.g., dwelltime). The material in target surface (e.g., powder material such as ina top surface of a powder bed) can absorb the energy from the energybeam and, and as a result, a localized region of at least the materialat the target surface can increase in temperature. The energy beam canbe moveable such that it may translate (e.g., horizontally, vertically,and/or in an angle). The energy source may be movable such that it cantranslate relative to the target surface. The energy beam can be movedvia a scanner (e.g., as disclosed herein). A least two (e.g., all) ofthe energy beams can be movable with the same scanner. At least two ofthe energy source(s) and/or beam(s) can be translated independently ofeach other. In some cases, at least two of the energy source(s) and/orbeam(s) can be translated at different rates (e.g., velocities). In somecases, at least two of the energy beams can be comprise at least onedifferent characteristic. The characteristics may comprise wavelength,charge, power density, amplitude, trajectory, footprint, cross-section,focus, intensity, energy, path, or hatching scheme. The charge can beelectrical and/or magnetic charge. In some embodiments, the energysource may be non-translatory (e.g., during the 3D printing). The energysource may be (e.g., substantially) stationary (e.g., before, afterand/or during the 3D printing). In some embodiments, the energy sourcemay translate (e.g., before, after and/or during the 3D printing).

In some embodiments, the energy source includes an array, or a matrix,of energy sources (e.g., laser diodes). At least two (e.g., each) of theenergy sources in the array or matrix, can be independently controlled(e.g., by a control mechanism) such that the energy beams can be turnedoff and on independently. At least two of the energy sources (e.g., inthe array or matrix) can be collectively controlled such that the atleast two (e.g., all) of the energy sources can be turned off and onsimultaneously. The energy per unit area or intensity of at least twoenergy sources in the matrix or array can be modulated independently(e.g., by a controller). At times, the energy per unit area or intensityof at least two (e.g., all) of the energy sources (e.g., in the matrixor array) can be modulated collectively (e.g., by a controller). Thecontrol may be manual or automatic. The control may be before, after,and/or during the 3D printing.

In some embodiments, the energy beam translates with respect to thetarget surface. An optical mechanism (e.g., scanner) may facilitate atranslation of the energy beam can along the target surface. The energybeam can scan along the target surface by mechanical movement of theenergy source(s), one or more adjustable reflective mirrors, one or morepolygon light scanners, or any combination or permutation thereof. Theenergy source(s) can project energy to the target surface using a DLPmodulator, a one-dimensional scanner, a two-dimensional scanner, or anycombination thereof The energy source(s) can be stationary. The materialbed (e.g., target surface) may translate vertically, horizontally, or inan angle (e.g., planar or compound). The translation may be effectuatedusing one or more motors. The translation may be effectuated using amechanically moving stage.

In some embodiments, the energy source and/or beam is moveable such thatit can translate relative to the target surface (e.g., material bed). Insome instances, the energy source and/or beam may be movable such thatit can translate across (e.g., laterally) the exposed (e.g., top)surface of the material bed. The energy beam(s) can be moved via ascanner. The scanner may comprise a galvanometer scanner, a polygon, amechanical stage (e.g., X-Y stage), a piezoelectric device, gimble, orany combination of thereof The galvanometer may comprise a mirror. Thescanner may comprise a modulator. The scanner may comprise a polygonalmirror. The scanner can be the same scanner for two or more energysources and/or beams. The scanner may comprise an optical setup. Atleast two (e.g., each) energy beams may have a separate scanner. Theenergy sources can be translated independently of each other. In somecases, at least two energy sources and/or beams can be translated atdifferent rates, and/or along different paths. For example, the movementof the first energy source may be faster (e.g., greater rate) ascompared to the movement of the second energy source. For example, themovement of the first energy beam may be faster (e.g., greater rate) ascompared to the movement of the second energy beam. The systems and/orapparatuses disclosed herein may comprise one or more shutters (e.g.,safety shutters). The energy beam(s), energy source(s), and/or theplatform can be moved (as applicable, e.g., by a motor, e.g., by thescanner.). The galvanometer scanner may comprise a two-axis galvanometerscanner. The scanner may comprise a modulator (e.g., as describedherein). The energy source(s) can project energy using a DLP modulator,a one-dimensional scanner, a two-dimensional scanner, or any combinationthereof The energy source(s) can be stationary or translatable. Theenergy source(s) can translate vertically, horizontally, or in an angle(e.g., planar or compound angle). The translation may be before, after,and/or during at least a portion of the 3D printing. The translation maybe controlled manually and/or automatically (e.g., by a controller). Theenergy source(s) can be modulated. The scanner can be included in,and/or can comprise, an optical system (e.g., optical setup, or opticalmechanism) that is configured to direct energy from the energy source toa predetermined position on the target surface (e.g., exposed surface ofthe material bed). The controller can be programmed to control atrajectory of the energy source(s) with the aid of the optical system.The controller can regulate a supply of energy from the energy source tothe material (e.g., at the target surface) to form a transformedmaterial. The controller may operate before, after, and/or during atleast a portion of the 3D printing (e.g., in real-time).

In some embodiments, the energy source is modulated. The energy beamemitted by the energy source can be modulated. The modulator can includeamplitude modulator, phase modulator, or polarization modulator. Themodulation may alter the intensity and/or power density of the energybeam. The modulation may alter the current supplied to the energy source(e.g., direct modulation). The modulation may affect the energy beam(e.g., external modulation such as external light modulator). Themodulation may include direct modulation (e.g., by a modulator). Themodulation may include an external modulator. The modulator can includean aucusto-optic modulator or an electro-optic modulator. The modulatorcan comprise an absorptive modulator or a refractive modulator. Themodulation may alter the absorption coefficient the material that isused to modulate the energy beam. The modulator may alter the refractiveindex of the material that is used to modulate the energy beam. Thefocus of the energy beam may be controlled (e.g., modulated). Themodulation may be controlled (e.g., manually and/or automatically). Themodulation may be controlled before, after, and/or during at least aportion of the 3D printing (e.g., in real-time).

In some embodiments, the apparatus and/or systems disclosed herein mayinclude an optical diffuser. The optical diffuser may diffuse light(e.g., substantially) homogenously. The optical diffuser may remove highintensity energy (e.g., light) distribution and form a more evendistribution of light across the footprint of the (e.g., transforming)energy beam. The optical diffuser may reduce the intensity of the energybeam (e.g., act as a screen). For example, the optical diffuser mayalter an energy beam with Gaussian profile, to an energy beam having atop-hat profile. The optical diffuser may comprise a diffuser wheelassembly. The energy profile alteration device may comprise adiffuser-wheel (a.k.a., diffusion-wheel). The diffuser-wheel maycomprise a filter wheel. The diffuser-wheel may comprise a filter ordiffuser. The diffuser-wheel may comprise multiple filters and/ormultiple diffusers. The filters and/or diffusers in the diffuser-wheelmay be arranged linearly, non-linearly, or any combination thereof Theenergy profile alteration device and/or any of its components may becontrolled (e.g., monitored and/or regulated), and be operativelycoupled thereto. The control may be manual and/or automatic (e.g., by acontroller). The control may be before, after, and/or during at least aportion of the 3D printing. The diffuser-wheel may comprise one or moreports (e.g., opening and/or exit ports) from/to which an energy ray(e.g., beam and/or flux) may travel. The diffuser-wheel may comprise apanel. The panel may block (e.g., entirely or partially) the energybeam. The energy profile alteration device may comprise a shutter wheel.In some examples, the diffuser-wheel (e.g., controllably) rotates. Insome examples, the diffuser-wheel may (e.g., controllably) switch (e.g.,alternate) between several positions. A position of the diffuser-wheelmay correspond to a filter. The filter may be maintained during theformation of a layer of hardened material or a portion thereof. Thefilter may change during the formation of a layer of hardened materialor a portion thereof. The diffuser-wheel may change between positionsduring the formation of a layer of hardened material or a portionthereof (e.g., change between at least 2, 3, 4, 5, 6, 7 positions). Thediffuser-wheel may maintain a position during the formation of a layerof hardened material or a portion thereof. Sometimes, during theformation of a 3D object, some positions of the diffuser-wheel may notbe used. At times, during the formation of a 3D object, all thepositions of the diffuser-wheel may be used.

The energy beam has one or more characteristics. The energy beam (e.g.,transforming energy beam) may comprise a Gaussian energy beam. Theenergy beam may have any cross-sectional shape comprising an ellipse(e.g., circle), or a polygon The energy beam may have a cross sectionwith a FLS of any value between the afore-mentioned values (e.g., fromabout 50 μm to about 250 μm, from about 50 μm to about 150 μm, or fromabout 150 μm to about 250 μm). The energy beam may be continuous ornon-continuous (e.g., pulsing). The energy beam may be modulated beforeand/or during the formation of a transformed material as part of the 3Dobject. The energy beam may be modulated before and/or during the 3Dprinting process.

The tiling energy flux may comprise (i) an extended exposure area, (ii)extended exposure time, (iii) low power density (e.g., power per unitarea) or (iv) an intensity profile that can fill an area with a flat(e.g., top head) energy profile. Extended may be in comparison with thescanning energy beam. The extended exposure time may be at least about 1millisecond and at most 100 milliseconds. In some embodiments, an energyprofile of the tiling energy source may exclude a Gaussian beam or roundtop beam. In some embodiments, an energy profile of the tiling energysource may include a Gaussian beam or round top beam. In someembodiments, the 3D printer comprises a first and/or second scanningenergy beams. In some embodiments, an energy profile of the first and/orsecond scanning energy may comprise a Gaussian energy beam. In someembodiments, an energy profile of the first and/or second scanningenergy beam may exclude a Gaussian energy beam. The first and/or secondscanning energy beam may have any cross-sectional shape comprising anellipse (e.g., circle), or a polygon (e.g., as disclosed herein). Thescanning energy beam may have a cross section with a diameter of atleast about 50 micrometers (μm), 100 μm, 150 μm, 200 μm, or 250 μm. Thescanning energy beam may have a cross section with a diameter of at mostabout 60 micrometers (μm), 100 μm, 150 μm, 200 μm, or 250 μm. Thescanning energy beam may have a cross section with a diameter of anyvalue between the afore-mentioned values (e.g., from about 50 μm toabout 250 μm, from about 50 μm to about 150 μm, or from about 150 μm toabout 250 μm). The power density (e.g., power per unit area) of thescanning energy beam may at least about 5000 W/mm², 10000 W/mm², 20000W/mm², 30000 W/mm², 50000 W/mm², 60000 W/mm², 70000 W/mm², 80000 W/mm²,90000 W/mm², or 100000 W/mm². The power density of the scanning energybeam may be at most about 5000 W/mm², 10000 W/mm², 20000 W/mm², 30000W/mm², 50000 W/mm², 60000 W/mm², 70000 W/mm², 80000 W/mm², 90000 W/mm²,or 100000 W/mm². The power density of the scanning energy beam may beany value between the afore-mentioned values (e.g., from about 5000W/mm² to about 100000 W/mm², from about 10000 W/mm² to about 50000W/mm², or from about 50000 W/mm² to about 100000 W/mm²). The scanningspeed of the scanning energy beam may be at least about 50 millimetersper second (mm/sec), 100 mm/sec, 500 mm/sec, 1000 mm/sec, 2000 mm/sec,3000 mm/sec, 4000 mm/sec, or 50000 mm/sec. The scanning speed of thescanning energy beam may be at most about 50 mm/sec, 100 mm/sec, 500mm/sec, 1000 mm/sec, 2000 mm/sec, 3000 mm/sec, 4000 mm/sec, or 50000mm/sec. The scanning speed of the scanning energy beam may any valuebetween the afore-mentioned values (e.g., from about 50 mm/sec to about50000 mm/sec, from about 50 mm/sec to about 3000 mm/sec, or from about2000 mm/sec to about 50000 mm/sec). The scanning energy beam may becontinuous or non-continuous (e.g., pulsing). In some embodiments, thescanning energy beam compensates for heat loss at the edges of thetarget surface after the heat tiling process (e.g., forming the tiles byutilizing the tiling energy beam).

In some embodiments, the tiling energy beam has an extended crosssection. For example, the tiling energy beam has a FLS (e.g., crosssection) that is larger than the scanning energy beam. The FLS of across section of the tiling energy beam may be at least about 0.2millimeters (mm), 0.3 mm, 0.4 mm, 0.5 mm, 0.8 mm, 1 mm, 1.5 mm, 2 mm,2.5 mm, 3 mm, 3.5 mm, 4 mm, 4.5 mm, or 5 mm. The FLS of a cross sectionof the tiling energy beam may be between any of the afore-mentionedvalues (e.g., from about 0.2 mm to about 5 mm, from about 0.3 mm toabout 2.5 mm, or from about 2.5 mm to about 5 mm). The cross section ofthe tiling energy beam can be at least about 0.1 millimeter squared(mm²), or 0.2. The diameter of the tiling energy beam can be at leastabout 300 micrometers, 500 micrometers, or 600 micrometers. The distancebetween the first position and the second position can be at least about100 micrometers, 200 micrometers, or 250 micrometers. The FLS may bemeasured at full width half maximum intensity of the energy beam. TheFLS may be measured at 1/e² intensity of the energy beam. In someembodiments, the tiling energy beam is a focused energy beam. In someembodiments, the tiling energy beam is a defocused energy beam. Theenergy profile of the tiling energy beam may be (e.g., substantially)uniform (e.g., in the beam cross sectional area that forms the tile).The energy profile of the tiling energy beam may be (e.g.,substantially) uniform during the exposure time (e.g., also referred toherein as tiling time, or dwell time). The exposure time (e.g., at thetarget surface) of the tiling energy beam may be at least about 0.1milliseconds (msec), 0.5 msec, 1 msec, 10 msec, 20 msec, 30 msec, 40msec, 50 msec, 60 msec, 70 msec, 80 msec, 90 msec, 100 msec, 200 msec,400 msec, 500 msec, 1000 msec, 2500 msec, or 5000 msec. The exposuretime (e.g., at the target surface) of the tiling energy beam may be atmost about 10 msec, 20 msec, 30 msec, 40 msec, 50 msec, 60 msec, 70msec, 80 msec, 90 msec, 100 msec, 200 msec, 400 msec, 500 msec, 1000msec, 2500 msec, or 5000 msec. The exposure time may be between any ofthe above-mentioned exposure times (e.g., from about 0.1 msec to about5000 msec, from about 0.1 to about 1 msec, from about 1 msec to about 50msec, from about 50 msec to about 100 msec, from about 100 msec to about1000 msec, from about 20 msec to about 200 msec, or from about 1000 msecto about 5000 msec). The exposure time may be the dwell time. The powerper unit area of the tiling energy beam may be at least about 100 Wattsper millimeter square (W/mm²), 200 W/mm², 300 W/mm², 400 W/mm², 500W/mm², 600 W/mm², 700 W/mm², 800 W/mm², 900 W/mm², 1000 W/mm², 2000W/mm², 3000 W/mm², 5000 W/mm2, or 7000 W/mm². The power per unit area ofthe tiling energy beam may be at most about 100 W/mm², 200 W/mm², 300W/mm², 400 W/mm², 500 W/mm², 600 W/mm², 700 W/mm², 800 W/mm², 900 W/mm²,1000 W/mm², 2000 W/mm², 3000 W/mm², 5000 W/mm², 7000 W/mm², 8000 W/mm²,9000 W/mm², or 10000 W/mm². The power per unit area of the tiling energybeam may be any value between the afore-mentioned values (e.g., fromabout 100 W/mm² to about 3000 W/mm², from about 100 W/mm² to about 5000W/mm², from about 100 W/mm² to about 9000 W/mm², from about 100 W/mm² toabout 500 W/mm², from about 500 W/mm² to about 3000 W/mm², from about1000 W/mm² to about 7000 W/mm², or from about 500 W/mm² to about 8000W/mm²). The tiling energy beam may emit energy stream towards the targetsurface in a step and repeat sequence.

In some embodiments, the tiling energy source is the same as thescanning energy source. In some embodiments, the tiling energy source isdifferent than the scanning energy source. The tiling energy sourceand/or scanning energy source can be disposed within the enclosure,outside of the enclosure, or within at least one wall of the enclosure.The optical mechanism through which the tiling energy flux and/or thescanning energy beam travel can be disposed within the enclosure,outside of the enclosure, or within at least one wall of the enclosure.

Energy may be evacuated from the material bed. The evacuation of energymay utilize a cooling member. Energy (e.g., heat) can be transferredfrom the material bed to a cooling member (e.g., heat sink FIG. 1, 113).The cooling member is described in Provisional Patent Application Ser.No. 62/265,817, filed on Dec. 10, 2015,” and Provisional PatentApplication No. 62/317,070, field on Apr. 1, 2016, both titled“APPARATUSES, SYSTEMS AND METHODS FOR EFFICIENT THREE-DIMENSIONALPRINTING;” and in Patent Application serial number PCT/US16/66000, filedon Dec. 9, 2016, titled “SKILLFUL THREE-DIMENSIONAL PRINTING,” all threeof which are incorporated herein by reference in their entirety.

In some embodiments, a layer dispensing mechanism dispenses thepre-transformed material (e.g., towards the platform), planarizes,distributes, spreads, and/or removes the pre-transformed material (e.g.,in the material bed). The layer dispensing mechanism may be utilized to(e.g., layerwise) form the material bed. The layer dispensing mechanismmay be utilized to form the layer of pre-transformed material (or aportion thereof). The layer dispensing mechanism may be utilized tolevel (e.g., planarize) the layer of pre-transformed material (or aportion thereof). The leveling may be to a predetermined height. Thelayer dispensing mechanism may comprise at least one, two or three of a(i) material dispensing mechanism (e.g., FIG. 1, 116), (ii) materialleveling mechanism (e.g., FIG. 1, 117), and (iii) material removalmechanism (e.g., FIG. 1, 118). The material removal mechanism maycomprise a cyclonic separator (e.g., a cyclonic separation system). Thecyclonic separator may separate pre-transformed material (e.g., powder),from one or more gasses that carry the pre-transformed material into thematerial removal mechanism (e.g., into the cyclonic separator). Thepre-transformed material may be a particulate (e.g., powder) material.The layer dispensing mechanism may be controlled manually and/or by thecontroller (e.g., before, after, and/or during the 3D printing). Thelayer dispensing mechanism and any of its components can be any of thosedisclosed in patent application No. 62/265,817, or patent applicationnumber PCT/US15/36802, both of which are incorporated herein byreference in their entirety. The layer dispensing system may comprise ahopper. The layer dispensing system may comprise (e.g., may be) arecoater.

In some embodiments, one or more sensors (at least one sensor) detectthe topology of the exposed surface of the material bed and/or theexposed surface of the 3D object (or any portion thereof). The sensorcan detect the amount of pre-transformed material deposited in thematerial bed. The sensor can comprise a proximity sensor. For example,the sensor may detect the amount of pre-transformed (e.g., powder)material deposited on the platform and/or on the exposed surface of amaterial bed. The sensor may detect the physical state of materialdeposited on the target surface (e.g., liquid or solid (e.g., powder orbulk)). The sensor be able to detect the microstructure (e.g.,crystallinity) of the pre-transformed material deposited on the targetsurface. The sensor may detect the amount of pre-transformed materialdisposed by the layer dispensing mechanism (e.g., powder dispenser). Thesensor may detect the amount of pre-transformed material that isrelocated by the layer dispensing mechanism (e.g., by the levelingmechanism). The sensor can detect the temperature of the pre-transformedand/or transformed material in the material bed. The sensor may detectthe temperature of the pre-transformed material in a material (e.g.,powder) dispensing mechanism, and/or in the material bed. The sensor maydetect the temperature of the pre-transformed material during and/orafter its transformation. The sensor may detect the temperature and/orpressure of the atmosphere within the enclosure (e.g., chamber). Thesensor may detect the temperature of the material (e.g., powder) bed atone or more locations.

In some embodiments, a topological map is formed using at least onemetrological sensor. The metrological sensor may comprise projection ofa static or time varying oscillating (e.g., striped) pattern. Themetrological sensor may comprise a fringe projection profilometrydevice. The metrological sensor may be at least a part of the heightmapper. The metrological sensor may comprise an emitter generating asensing energy beam (e.g., emitter as in FIG. 3, 317) and a receiver(e.g., FIG. 3, 318). The emitter may comprise a projector. The emittermay project the sensing energy beam on a target surface. The targetsurface may comprise an exposed surface of a material bed, a layer ofhardened material, a 3D object, and/or a melt pool. The sensing energybeam may form a pattern on the target (e.g., exposed) surface. Thepattern may comprise areas of various levels of light intensity. FIGS.21A-21D show various light intensity profiles as a function of time. Thelight intensity profile may comprise an on off pattern (e.g., FIG. 21A).The light intensity profile may comprise a fluctuating pattern. Thefluctuating pattern may comprise gradually fluctuating intensity pattern(e.g., FIG. 21B) or abruptly fluctuating intensity pattern (e.g., FIG.21A). The fluctuating pattern may comprise a superposition of amultiplicity of sinusoidal waves (e.g., FIG. 21D). The fluctuatingpattern may comprise a superposition of a multiplicity of frequencyfunctions (e.g., sine function and/or cosine function). The fluctuatingpattern may comprise a superposition of a sinusoidal wave and adecreasing function (e.g., 21C). The decreasing function may bedecreasing linearly, logarithmically, exponentially, or any combinationthereof. The fluctuating pattern may comprise multiplicity of functions(e.g., that are superpositioned). The multiplicity of functions may beshifted (e.g., by a phase and/or fringe). The multiplicity of functionsmay be shifted (e.g., by a phase and/or fringe) with respect to eachother. At least two of the multiplicity of functions (e.g., all of thefunctions) may be shifted (e.g., by a phase and/or fringe) collectively.In some examples, the fluctuating pattern are shifted (e.g., by a phaseand/or fringe). For example, the fluctuating pattern may be shiftedduring the use of the metrological detector (e.g., height mapper). Forexample, the fluctuating pattern may be shifted during the operation of(e.g., detection by) the metrological detector. The shift may be of atleast a portion of a (e.g., a whole) wavelength (λ) of the sensingenergy beam. The shift may by at least about λ/10, λ/9, λ/8, λ/7, λ/6,λ/5, λ/4, λ/3, or λ/2. The shift may by at most about λ/10, λ/9, λ/8,λ/7, λ/6, λ/5, λ/4, λ/3, or λ/2. The shift may by any value between theafore-mentioned values (e.g., from about λ to about λ/10, from about λ/2to about λ/10, from about λ/2 to about λ/5, from about λ/5 to aboutλ/10, or from about λ/2 to about λ/4,). The fluctuating pattern may beshifted by (e.g., substantially) the same (e.g., delta) value across thetarget surface. The fluctuating pattern may be shifted by differentvalues across the target surface. For example, at least a first area ofthe target surface may be sensed with a shifting fluctuating pattern byabout λ/3, and at least a second area of the target surface (thatdiffers from the first area) may be sensed by a shifting fluctuatingpattern by about λ/5. The fluctuating pattern may be shifted (i) by afirst value across the target surface at a first time (or firsttime-period), and (ii) by a second value across the target surface at asecond time (or second time-period). For example, the target surface maybe sensed with a shifting and fluctuating pattern that is of λ/3 at timeperiod t₁, and the target surface may be sensed by a shiftingfluctuating pattern that is of λ/5 at time period t₂ (that differs fromt₁). In some embodiments, the use of a certain shift in the fluctuatingpattern at a certain area of the target surface relates to a certainsensitivity (e.g., resolution) of detection at that certain area. Theuse of different shift values in the fluctuating pattern at differentareas of the target surface may allow detection of these different areasat a different sensitivity (e.g., resolution). The different shift inthe fluctuating pattern may correlate to the different in materialproperties (e.g., phases). For example, a different shift value may beused on a target surfaced area comprising a pre-transformed material,than on a target surface area comprising a transformed material. Thedetector may comprise a multiplicity of sensing energy beams. Themultiplicity of energy beams may form an interference pattern. Thefluctuating pattern may comprise an interference pattern. The projectedsensing energy beams may be of the same or of different colors. At leasttwo of the projected sensing energy beams may be of the same or of(e.g., substantially) the same color. At least two of the projectedsensing energy beams may be of different colors. The projected sensingenergy beams may be of the same or of different frequencies. At leasttwo of the projected sensing energy beams may be of differentfrequencies. At least two of the projected sensing energy beams may beof the same or of (e.g., substantially) the same frequency. The variousmultiplicity of projected sensing energy beams may be projectedsimultaneously or sequentially. At least two of the projected sensingenergy beams may be of projected sequentially. At least two of theprojected sensing energy beams may be projected (e.g., substantially)simultaneously. Substantial may be relative to the effect on thedetection (e.g., effect on the resolution of the detection). Thefluctuating pattern may scan the target surface (e.g., by projecting oneor more shapes). At times, the fluctuating pattern may be apparent on atleast a portion of the target surface (e.g., FIG. 19, showingfluctuating rectangles (e.g., thick lines) of various intensities). Insome embodimetns the fluctuating pattern is detectable (e.g., mayappear) on at least a portion of the target surface, wherein fluctuatingintensity pattern is presented as a function of location (e.g., of atleast a portion of the target surface). The fluctuating positionalintensity function may be similar to the functions shown in FIGS.21A-21B, whrein the “Time” label is changed to a “Position” label.Additionally or alternatively, the fluctuating positional pattern maychange as a function of time (e.g., as shown in FIGS. 21A-21B).

In some embodiments, the (e.g., metrological or temperature) sensor (ordetector) comprises a filter (e.g., FIG. 3, 326). The energy beam thatis used in transforming the pre-transformed material to a transformedmaterial (e.g , scanning energy beam and/or tiling energy beam) may bereferred to herein as the “transforming energy beam.” The filter mayfilter a sensing energy beam from the transforming energy beam (e.g.,FIG. 3, 340). The sensing energy beam may comprise electromagneticradiation (e.g., from a light emitting diode). The sensing energy beammay comprise collimated or non-collimated light. The filtering may beperformed before, during and/or after building a 3D object. Filteringmay reduce the amount of transforming energy beam that is sensed by thesensor. Filtering may protect the sensor from the transforming energybeam (e.g., having high intensity), e.g., during building of the 3Dobject. The filtering may allow measuring the sensing energy beam inreal time during operation of the transforming energy beam (e.g.,forming at least a portion of the 3D object). Additionally, filteringmay allow sensing and/or detecting in real-time (e.g., during build ofthe 3D object). FIG. 29 shows an example of a sensing energy beam 2908that is separated from the transforming energy beam 2901. FIG. 29 showsan example of a processing chamber (e.g., having a wall 2907 and anatmosphere 2926) that is engaged with a build module (e.g., 2940) toform an enclosure. The build module may include a target surface (e.g.,2910). The 3D object may be built in a material bed 2904 by irradiatingit with a transforming energy beam (e.g., 2901). FIG. 29 further shows asensing energy beam (e.g., 2908) that is irradiated on the targetsurface. The sensing energy beam may be used to sense a characteristicof one or more positions of the target surface (e.g., of the building 3Dobject). The sensing energy beam may be generated by a light energysource (e.g., FIG. 29, 2922, e.g., LED lamp). The light source maycomprise a digital light projector. The light source may comprise adigital light imager. The metrology detection system may comprisedigital light processing. The light source may comprise a digital mirror(e.g., micro-mirror) device. The light source may comprise a lens (e.g.,a lens array). The light source may comprise a mirror (e.g., microscopicmirror). The light source may comprise an array (e.g., of microscopic)mirrors. The array may be rectangular. The mirror in the array may bemovable (e.g., controllably). The control may comprise electric (e.g.,electrostatic) control. The light source may comprise amicro-opto-electromechanical system (e.g., a digital micromirror device,or DMD). The mirror may comprise silicon or aluminum. The digital lightprojector may comprise a digital micromirror device.

The sensing energy beam may comprise a wavelength different than thetransforming energy beam. The sensing energy beam may comprise awavelength that is below a thermal radiative beam (e.g., below red orinfra-red radiation). The sensing energy beam may comprise a wavelengththat is above a plasma generating radiation (e.g., above ultravioletradiation, e.g., from a purple to an orange visible light radiation).The wavelength of the sensing energy beam may be above about 100 nm, 200nm, 300 nm, 350 nm, 400 nm, 450 nm, 500 nm, 550 nm, 600 nm, or 650 nm.The wavelength of the sensing energy beam may be below about 1000 nm,950 nm, 900 nm, 850 nm, 800 nm, 750 nm, or 700 nm. The wavelength of thesensing energy beam may be any wavelength between the afore-mentionedwavelengths (e.g., from 100 nm to 1000 nm, from 300 nm to 800 nm, orfrom 400 nm to 500 nm). The sensing energy may be any energy beamdescribed herein. At times, the transforming energy beam (e.g., 2901)may be projected through a first optical window (e.g., 2915). Thesensing energy beam may be projected (e.g., optionally) through a secondoptical window (e.g., 2918). In some embodiments, the first and secondoptical window are the same optical window. In some embodiments, thefirst optical window is different than the second optical window. Theenergy beam reflected from the target surface (e.g., 2930) that reachesa receiver (e.g., 2925, a detector), may travel through the firstoptical window (e.g., 2915) and/or the second optical window (e.g.,2918). The detector may be (e.g., atmospherically) separated from theprocessing chamber by the optical window (e.g., 2925). At times, thedetector may have the same atmosphere as the processing chamber (e.g.,FIGS. 3, 318 and 317). The first and/or second optical window may have acoating on at least one of their respective surfaces. For example, thefirst and/or second optical window may have a coating at least on itssurface that face the interior of the processing chamber (e.g., FIG. 29,2926). The coating may comprise an anti-reflective, dielectric,wavelength filtering, transparent, conductive, and/or atransparent-conductive coating. The wavelength filtering coating maycomprise an ultraviolet (e.g., extreme ultraviolet) filtering coating.At times, the coating may be applied on both surfaces of the opticalwindow.

In some embodiments, the detection system comprises a multiplicity ofdetection systems (e.g., a multiplicity of receivers and/ortransmitters). The multiplicity of receivers and/or transmitters mayview the target location from a multiplicity of spatial position. Themultiplicity of spatial positions may form a multi perspective image.Examples of a multiplicity of detection systems can be seen in PatentApplication serial number PCT/US15/65297, filed on Dec. 11 2015, titled“FEEDBACK CONTROL SYSTEMS FOR THREE-DIMENSIONAL PRINTING,” which isfully incorporated herein by reference.

In some embodiments, at least one sensor is operatively coupled to acontrol system (e.g., computer control system). The sensor may compriselight sensor, acoustic sensor, vibration sensor, chemical sensor,electrical sensor, magnetic sensor, fluidity sensor, movement sensor,speed sensor, position sensor, pressure sensor, force sensor, densitysensor, distance sensor, or proximity sensor. The sensor may comprisetemperature sensor, weight sensor, material (e.g., powder) level sensor,metrology sensor, gas sensor, or humidity sensor. The metrology sensormay comprise a measurement sensor (e.g., height, length, width, angle,and/or volume). The metrology sensor may comprise a magnetic,acceleration, orientation, or optical sensor. The sensor may transmitand/or receive sound (e.g., echo), magnetic, electronic, and/orelectromagnetic signal. The electromagnetic signal may comprise avisible, infrared, ultraviolet, ultrasound, radio wave, or microwavesignal. The metrology sensor may measure a vertical, horizontal, and/orangular position of at least a portion of the target surface. Themetrology sensor may measure a gap. The metrology sensor may measure atleast a portion of the layer of material. The layer of material may be apre-transformed material (e.g., powder), transformed material, orhardened material. The metrology sensor may measure at least a portionof the 3D object. The metrology sensor may measure the FLS (e.g., depth)of at least one melt pool. The metrology sensor may measure a height ofa 3D object that protrudes from the exposed surface of the material bed.The metrology sensor may measure a height of a 3D object that deviatesfrom the average and/or mean of the exposed surface of the material bed.The gas sensor may sense any of the gas. The distance sensor can be atype of metrology sensor. The distance sensor may comprise an opticalsensor, or capacitance sensor. The temperature sensor can compriseBolometer, Bimetallic strip, Calorimeter, Exhaust gas temperature gauge,Flame detection, Gardon gauge, Golay cell, Heat flux sensor, Infraredthermometer, Microbolometer, Microwave radiometer, Net radiometer,Quartz thermometer, Resistance temperature detector, Resistancethermometer, Silicon band gap temperature sensor, Special sensormicrowave/imager, Temperature gauge, Thermistor, Thermocouple,Thermometer (e.g., resistance thermometer), or Pyrometer. Thetemperature sensor may comprise an optical sensor. The temperaturesensor may comprise image processing. The temperature sensor may becoupled to a processor that would perform image processing by using atleast one sensor generated signal. The temperature sensor may comprise acamera (e.g., IR camera, CCD camera).

In some embodiments, the light sensor comprises a semi conductivedevice. The light sensor may comprise p-doped metal-oxide-semiconductor(MOS), or complementary MOS (CMOS). In some embodiments, the lightsensor comprises a material that is sensitive to light. The materialsensitive to light may alter at least one of its properties as aresponse to incoming light photos. For example, the material sensitiveto light may alter its temperature, color, refractive index, electricalconductivity, magnetic field, and/or volume as a response to incominglight photos. The material sensitive to light may alter the energy levelpopulation of its electrons as a response to incoming light photons. Thealternation may take place in the areas which were exposed to the light(e.g., areas which absorbed the photons).

In some embodiments, the systems and/or apparatuses described hereincomprise a temperature sensor. The temperature sensor may comprise a gassensor. The temperature sensor may be sensitive to a radiation (e.g.,electromagnetic radiation) having a wavelength of at least about 0.5 μm,1 μm, 1.5 μm, 2.5 μm, 3 μm, 3.5 μm, 4 μm, 4.5 μm, 5 μm, 5.5 μm, 6 μm,6.5 μm, 7 μm, 8 μm, or 9 μm. The temperature sensor may be sensitive toa radiation (e.g., electromagnetic radiation) having a wavelength of anyvalue between the afore-mentioned values (e.g., from about 0.5 μm toabout 9 μm, from about 0.5 μm to about 3 μm, from about 1 μm to about 5μm, from about 1 μm to about 2.5 μm, or from about 5 μm to about 9 μm).The pressure sensor may comprise Barograph, Barometer, Boost gauge,Bourdon gauge, Hot filament ionization gauge, Ionization gauge, McLeodgauge, Oscillating U-tube, Permanent Downhole Gauge, Piezometer, Piranigauge, Pressure sensor, Pressure gauge, Tactile sensor, or Time pressuregauge. The position sensor may comprise Auxanometer, Capacitivedisplacement sensor, Capacitive sensing, Free fall sensor, Gravimeter,Gyroscopic sensor, Impact sensor, Inclinometer, Integrated circuitpiezoelectric sensor, Laser rangefinder, Laser surface velocimeter,LIDAR, Linear encoder, Linear variable differential transformer (LVDT),Liquid capacitive inclinometers, Odometer, Photoelectric sensor,Piezoelectric accelerometer, Rate sensor, Rotary encoder, Rotaryvariable differential transformer, Selsyn, Shock detector, Shock datalogger, Tilt sensor, Tachometer, Ultrasonic thickness gauge, Variablereluctance sensor, or Velocity receiver. The detector may comprise anarray of optical sensors. The optical sensor may comprise aCharge-coupled device, Colorimeter, Contact image sensor,Electro-optical sensor, Infra-red sensor, Kinetic inductance detector,light emitting diode (e.g., light sensor), Light-addressablepotentiometric sensor, Nichols radiometer, Fiber optic sensors, Opticalposition sensor, Photo detector, Photodiode, Photomultiplier tubes,Phototransistor, Photoelectric sensor, Photoionization detector,Photomultiplier, Photo resistor, Photo switch, Phototube,Scintillometer, Shack-Hartmann, Single-photon avalanche diode,Superconducting nanowire single-photon detector, Transition edge sensor,Visible light photon counter, or Wave front sensor. The weight of thematerial bed can be monitored by one or more weight sensors. The weightsensor(s) may be disposed in, and/or adjacent to the material bed. Aweight sensor disposed in the material bed can be disposed at the bottomof the material bed (e.g. adjacent to the platform). The weight sensorcan be between the bottom of the enclosure (e.g., FIG. 1, 111) and thesubstrate (e.g., FIG. 1, 109) on which the base (e.g., FIG. 1, 102) orthe material bed (e.g., FIG. 1, 104) may be disposed. The weight sensorcan be between the bottom of the enclosure and the base on which thematerial bed may be disposed. The weight sensor can be between thebottom of the enclosure and the material bed. A weight sensor cancomprise a pressure sensor. The weight sensor may comprise a springscale, a hydraulic scale, a pneumatic scale, or a balance. At least aportion of the pressure sensor can be exposed on a bottom surface of thematerial bed. The weight sensor can comprise a button load cell. Thebutton load cell can sense pressure from the pre-transformed material(e.g., powder) adjacent to the load cell. In an example, one or moresensors (e.g., optical sensors, e.g., optical level sensors) can beprovided adjacent to the material bed such as above, below, and/or tothe side of the material bed. In some examples, the one or more sensorscan sense the level (e.g., height and/or amount) of pre-transformedmaterial in the material bed. The pre-transformed material (e.g.,powder) level sensor can be in communication with a layer dispensingmechanism (e.g., powder dispenser). A sensor can be configured tomonitor the weight of the material bed by monitoring a weight of astructure that contains the material bed. One or more position sensors(e.g., height sensors) can measure the height of the material bedrelative to the platform (e.g., at one of more positions). The positionsensors can be optical sensors. The position sensors can determine adistance between one or more energy beams (e.g., a laser or an electronbeam.) and the exposed surface of the material (e.g., powder) bed. Theone or more sensors may be connected to a control system (e.g., to aprocessor and/or to a computer).

In some embodiments, the systems and/or apparatuses disclosed hereincomprise one or more motors. The motors may comprise servomotors. Theservomotors may comprise actuated linear lead screw drive motors. Themotors may comprise belt drive motors. The motors may comprise rotaryencoders. The apparatuses and/or systems may comprise switches. Theswitches may comprise homing or limit switches. The motors may compriseactuators. The motors may comprise linear actuators. The motors maycomprise belt driven actuators. The motors may comprise lead screwdriven actuators. The actuators may comprise linear actuators. Thesystems and/or apparatuses disclosed herein may comprise one or morepistons.

In some examples, a pressure system is in fluid communication with theenclosure. The pressure system can be configured to regulate thepressure in the enclosure. In some examples, the pressure systemincludes one or more pumps. The one or more pumps may comprise apositive displacement pump. The positive displacement pump may compriserotary-type positive displacement pump, reciprocating-type positivedisplacement pump, or linear-type positive displacement pump. Thepositive displacement pump may comprise rotary lobe pump, progressivecavity pump, rotary gear pump, piston pump, diaphragm pump, screw pump,gear pump, hydraulic pump, rotary vane pump, regenerative (peripheral)pump, peristaltic pump, rope pump, or flexible impeller. Rotary positivedisplacement pump may comprise gear pump, screw pump, or rotary vanepump. The reciprocating pump comprises plunger pump, diaphragm pump,piston pumps displacement pumps, or radial piston pump. The pump maycomprise a valveless pump, steam pump, gravity pump, eductor-jet pump,mixed-flow pump, bellow pump, axial-flow pumps, radial-flow pump,velocity pump, hydraulic ram pump, impulse pump, rope pump,compressed-air-powered double-diaphragm pump, triplex-style plungerpump, plunger pump, peristaltic pump, roots-type pumps, progressingcavity pump, screw pump, or gear pump.

In some examples, the pressure system includes one or more vacuum pumpsselected from mechanical pumps, rotary vain pumps, turbomolecular pumps,ion pumps, cryopumps, and diffusion pumps. The one or more vacuum pumpsmay comprise Rotary vane pump, diaphragm pump, liquid ring pump, pistonpump, scroll pump, screw pump, Wankel pump, external vane pump, rootsblower, multistage Roots pump, Toepler pump, or Lobe pump. The one ormore vacuum pumps may comprise momentum transfer pump, regenerativepump, entrapment pump, Venturi vacuum pump, or team ejector. Thepressure system can include valves; such as throttle valves. Thepressure system can include a pressure sensor for measuring the pressureof the chamber and relaying the pressure to the controller, which canregulate the pressure with the aid of one or more vacuum pumps of thepressure system. The pressure sensor can be coupled to a control system(e.g., controller). The pressure can be electronically or manuallycontrolled.

In some embodiments, the systems, apparatuses, and/or methods describedherein comprise a material recycling mechanism. The recycling mechanismcan collect at least unused pre-transformed material and return theunused pre-transformed material to a reservoir of a material dispensingmechanism (e.g., the material dispensing reservoir), or to a bulkreservoir that feeds the material dispensing mechanism. The recyclingmechanism and the bulk reservoir are described in patent application No.62/265,817, and patent application No. 62/317,070, both of which areincorporated herein by reference in their entirety.

In some cases, unused material (e.g., remainder) surrounds the 3D objectin the material bed. The unused material can be substantially removedfrom the 3D object. The unused material may comprise pre-transformedmaterial. Substantial removal may refer to material covering at mostabout 20%, 15%, 10%, 8%, 6%, 4%, 2%, 1%, 0.5%, or 0.1% of the surface ofthe 3D object after removal. Substantial removal may refer to removal ofall the material that was disposed in the material bed and remained aspre-transformed material at the end of the 3D printing process (i.e.,the remainder), except for at most about 10%, 3%, 1%, 0.3%, or 0.1% ofthe weight of the remainder. Substantial removal may refer to removal ofall the remainder except for at most about 50%, 10%, 3%, 1%, 0.3%, or0.1% of the weight of the printed 3D object. The unused material can beremoved to permit retrieval of the 3D object without digging through thematerial bed. For example, the unused material can be suctioned out ofthe material bed by one or more vacuum ports (e.g., nozzles) builtadjacent to the material bed, by brushing off the remainder of unusedmaterial, by lifting the 3D object from the unused material, by allowingthe unused material to flow away from the 3D object (e.g., by opening anexit opening port on the side(s) and/or on the bottom of the materialbed from which the unused material can exit). After the unused materialis evacuated, the 3D object can be removed. The unused pre-transformedmaterial can be re-circulated to a material reservoir for use in futurebuilds. The re-circulation can be before a new build, after completionof a build, and/or (e.g., continuously) during the 3D printing. Theremoval of the remainder may be effectuated as described in patentapplication No. 62/265,817, or in patent application numberPCT/US15/36802, both of which are incorporated herein by reference intheir entirety. In some cases, cooling gas can be directed to thehardened material (e.g., 3D object) for cooling the hardened materialduring and/or following its retrieval (e.g., from the build module).

In some cases, the 3D object is fabricated (e.g., printed) with a set oftransforming energy beams. The set of transforming energy beams maycomprise one or more transforming energy beams (e.g., scanning and/ortiling energy beam). The rate in which the set of set of transformingenergy beams fabricate the 3D object can be at least 1 cubic centimetersper hours (cm³/h), 5 cm³/h, 10 cm³/h, 20 cm³/h, 30 cm³/h, 40 cm³/h, 50cm³/h, 60 cm³/h, 70 cm³/h, 80 cm³/h, 90 cm³/h, 100 cm³/h, 110 cm³/h, 120cm³/h, 130 cm³/h, 140 cm³/h, or 150 cm³/h. The rate in which the set ofset of transforming energy beams fabricate the 3D object can be a valuebetween the afore-mentioned values (e.g., from about 1 cm³/h to about150 cm³/h, from about 20 cm³/h to about 120 cm³/h, from about 30 cm³/hto about 90 cm³/h, or from about 40 cm³/h to about 80 cm³/h).

In some examples, the final form of the 3D object is retrieved soonafter cooling of a final layer of hardened material. Soon after coolingmay be at most about 1 day, 12 hours (h), 6 h, 5 h, 4 h, 3 h, 2 h, 1 h,30 minutes, 15 minutes, 5 minutes, 240 s, 220 s, 200 s, 180 s, 160 s,140 s, 120 s, 100 s, 80 s, 60 s, 40 s, 20 s, 10 s, 9 s, 8 s, 7 s, 6 s, 5s, 4 s, 3 s, 2 s, or 1 s. Soon after cooling may be between any of theafore-mentioned time values (e.g., from about is to about 1 day, fromabout is to about 1 hour, from about 30 minutes to about 1 day, fromabout 20 s to about 240 s, from about 12 h to about 1 s, from about 12 hto about 30 min, from about 1 h to about 1 s, or from about 30 min toabout 40 s). In some cases, the cooling can occur by method comprisingactive cooling by convection using a cooled gas or gas mixturecomprising argon, nitrogen, helium, neon, krypton, xenon, hydrogen,carbon monoxide, carbon dioxide, or oxygen. Cooling may be cooling to ahandling temperature (e.g., ambient temperature). Cooling may be coolingto a temperature that allows a person to handle the 3D object.

In some examples, the generated 3D object requires very little or nofurther processing after its retrieval. In some examples, the diminishedfurther processing (or lack thereof), will afford a 3D printing processthat requires smaller amount of energy and/or less waste as compared tocommercially available 3D printing processes. The smaller amount can besmaller by at least about 1.1, 1.3, 1.5, 2, 3, 4, 5, 6, 7, 8, 9, or 10.The smaller amount may be smaller by any value between theafore-mentioned values (e.g., from about 1.1 to about 10, or from about1.5 to about 5). Further processing may comprise trimming (e.g.,ablating). Further processing may comprise polishing (e.g., sanding).The generated 3D object can be retrieved and finalized without removalof transformed material and/or auxiliary features (e.g., since the 3Dobject does not comprise any). The 3D object can be retrieved when the3D object, composed of hardened (e.g., solidified) material, is at ahandling temperature that is suitable to permit its removal from thematerial bed without its substantial deformation. The handlingtemperature can be a temperature that is suitable for packaging of the3D object. The handling temperature a can be at most about 120° C., 100°C., 80° C., 60° C., 40° C., 30° C., 25° C., 20° C., 10° C., or 5° C. Thehandling temperature can be of any value between the afore-mentionedtemperature values (e.g., from about 120° C. to about 20° C., from about40° C. to about 5° C., or from about 40° C. to about 10° C.).

In some embodiments, the methods, apparatuses, software, and systemsprovided herein result in fast and/or efficient formation of 3D objects.In some cases, the 3D object can be transported within at most about 120min, 100 min, 80 min, 60 min, 40 min, 30 min, 20 min, 10 min, or 5 minafter the last layer of the object hardens (e.g., solidifies). In somecases, the 3D object can be transported within at least about 120 min,100 min, 80 min, 60 min, 40 min, 30 min, 20 min, 10 min, or 5 min afterthe last layer of the object forms (e.g., hardens). In some cases, the3D object can be transported within any time between the above-mentionedvalues (e.g., from about 5 min to about 120 min, from about 5 min toabout 60 min, or from about 60 min to about 120 min). The 3D object canbe transported once it cools to a temperature of at most about 100° C.,90° C., 80° C., 70° C., 60° C., 50° C., 40° C., 30° C., 25° C., 20° C.,15° C., 10° C., or 5° C. The 3D object can be transported once it coolsto a temperature value between the above-mentioned temperature values(e.g., from about 5° C. to about 100° C., from about 5° C. to about 40°C., or from about 15° C. to about 40° C.). Transporting the 3D objectcan comprise packaging and/or labeling the 3D object. In some cases, the3D object can be transported directly to a consumer.

In some examples, the methods, systems, apparatuses, and/or softwarepresented herein facilitate formation of custom and/or a stock 3Dobjects for a customer. A customer can be an individual, a corporation,organization, government, non-profit organization, company, hospital,medical practitioner, engineer, retailer, any other entity, orindividual. The customer may be one that is interested in receiving the3D object and/or that ordered the 3D object. A customer can submit arequest for formation of a 3D object. The customer can provide an itemof value in exchange for the 3D object. The customer can provide adesign or a model for the 3D object. The customer can provide the designin the form of a stereo lithography (STL) file. The customer can providea design wherein the design can be a definition of the shape and/ordimensions of the 3D object in any other numerical or physical form. Insome cases, the customer can provide a 3D model, sketch, and/or image asa design of an object to be generated. The design can be transformed into instructions usable by the printing system to additively generate the3D object. The customer can provide a request to form the 3D object froma specific material or group of materials (e.g., a material as describedherein). In some cases, the design may not contain auxiliary features(or marks of any past presence of auxiliary support features). Inresponse to the customer request, the 3D object can be formed orgenerated with the printing method, system and/or apparatus as describedherein. In some cases, the 3D object can be formed by an additive 3Dprinting process (e.g., additive manufacturing). Additively generatingthe 3D object can comprise successively depositing and transforming(e.g., melting) a pre-transformed material (e.g., powder) comprising oneor more materials as specified by the customer. The 3D object can besubsequently delivered to the customer. The 3D object can be formedwithout generation or removal of auxiliary features (e.g., that isindicative of a presence or removal of the auxiliary support feature).Auxiliary features can be support features that prevent a 3D object fromshifting, deforming or moving during the formation of the 3D object.

In some examples, the 3D object is produced in a substantially accuratemanner, wherein substantially is relative to the intended purpose of the3D object. The 3D object (e.g., solidified material) that is generatedfor the customer can have an average deviation value from the intendeddimensions (e.g., specified by the customer, or designated according toa model of the 3D object) of at most about 0.5 microns (μm), 1 μm, 3 μm,10 μm, 30 μm, 100 μm, 300 μm, or less. The deviation can be any valuebetween the afore-mentioned values (e.g., from about 0.5 μm to about 300μm, from about 10 μm to about 50 μm, from about 15 μm to about 85 μm,from about 5 μm to about 45 μm, or from about 15 μm to about 35 μm). The3D object can have a deviation from the intended dimensions in aspecific direction, according to the formula Dv+L/K_(Dv), wherein Dv isa deviation value, L is the length of the 3D object in a specificdirection, and K_(Dv) is a constant. Dv can have a value of at mostabout 300 μm, 200 μm, 100 μm, 50 μm, 40 μm, 30 μm, 20 μm, 10 μm, 5 μm, 1μm, or 0.5 μm. Dv can have a value of at least about 0.5 μm, 1 μm, 3 μm,5 μm, 10 μm, 20 μm, 30 μm, 50 μm, 70 μm, 100 μm, or 300 μm. Dv can haveany value between the afore-mentioned values (e.g., from about 0.5 μm toabout 300 μm, from about 10 μm to about 50 μm, from about 15 μm to about85 μm, from about 5 μm to about 45 μm, or from about 15 μm to about 35μm). K_(DV) can have a value of at most about 3000, 2500, 2000, 1500,1000, or 500. K_(DV) can have a value of at least about 500, 1000, 1500,2000, 2500, or 3000. K_(DV) can have any value between theafore-mentioned values (e.g., from about 3000 to about 500, from about1000 to about 2500, from about 500 to about 2000, from about 1000 toabout 3000, or from about 1000 to about 2500).

In some examples, the intended dimensions of the 3D object are derivedfrom a model design of the 3D object. The 3D part can have the statedaccuracy value immediately after its formation, without additionalprocessing or manipulation. Receiving the order for the object,formation of the object, and delivery of the object to the customer cantake at most about 7 days, 6 days, 5 days, 3 days, 2 days, 1 day, 12hours, 6 hours, 5 hours, 4 hours, 3 hours, 2 hours, 1 hour, 30 min, 20min, 10 min, 5 min, 1 min, 30 seconds, or 10 seconds. Receiving theorder for the object, formation of the object, and delivery of theobject to the customer can take a period of time between any of theafore-mentioned time periods (e.g., from about 10 seconds to about 7days, from about 10 seconds to about 12 hours, from about 12 hours toabout 7 days, or from about 12 hours to about 10 minutes). In somecases, the 3D object can be generated in a period between any of theaforementioned time periods (e.g., from about lOseconds to about 7 days,from about 10 seconds to about 12 hours, from about 12 hours to about 7days, or from about 12 hours to about 10 minutes). The time can varybased on the physical characteristics of the object, including the sizeand/or complexity of the object.

In some embodiments, the system, methods, software, and/or apparatuscomprise at least one control mechanism (e.g., a controller). Themethods, systems, apparatuses, and/or software disclosed herein mayincorporate at least one controller that controls one or more of the(e.g., 3D printer) components described herein. In some embodiments, onecontroller controls two or more of the components. In some embodiments,at least two of the components are controlled by different controllers.The controller may comprise a computer-processing unit (e.g., acomputer) that is operatively coupled to any of the systems and/orapparatuses, or their respective components (e.g., the energysource(s)). Alternatively or additionally, the systems and/orapparatuses disclosed herein may be coupled to a processing unit.Alternatively or additionally, the methods and/or software mayincorporate the operation of a processing unit. The computer can beoperatively coupled through a wired and/or through a wirelessconnection. In some cases, the computer can be on board a user device. Auser device can be a laptop computer, desktop computer, tablet,smartphone, or another computing device. The controller can be incommunication with a cloud computer system and/or a server. Thecontroller can be programmed to (e.g., selectively) direct the energysource(s) to apply energy to the at least a portion of the targetsurface at a power per unit area. The controller can be in communicationwith the optical system (e.g., the scanner) configured to articulate theenergy source(s) to apply energy to at least a portion of the targetsurface at a power per unit area. The optical system may comprise anoptical setup.

The controller may control the layer dispensing mechanism and/or any ofits components. The controller may control the platform. The controllermay control the one or more sensors. The controller may control any ofthe components of the 3D printing system and/or apparatus. Thecontroller may control any of the mechanisms used to effectuate themethods described herein. The control may comprise controlling (e.g.,directing and/or regulating) the movement speed (velocity) of any of the3D printing mechanisms and/or components. The movement may behorizontal, vertical, and/or in an angle (planar and/or compound). Thecontroller may control at least one characteristic of the transformingenergy beam. The controller may control the movement of the transformingenergy beam (e.g., according to a path). The controller may control thesource of the (e.g., transforming and/or sensing) energy beam. Theenergy beam (e.g., transforming energy beam, and/or sensing energy beam)may travel through an optical setup. The optical setup may comprise amirror, a lens, a focusing device, a prism, or an optical window. FIG. 2shows an example of an optical setup in which an energy beam isprojected from the energy source 206, and is deflected by two mirrors205, and travels through an optical element 204. The optical element 204can be an optical window, in which case the incoming beam 207 issubstantially unaltered 203 after crossing the optical window. Theoptical element 204 can be a focus altering device (e.g., lens), inwhich case the focus (e.g., cross section) of the incoming beam 207 isaltered after passing through the optical element 204 and emerging asthe beam 203. The controller may control the scanner that directs themovement of the transforming energy beam and/or platform. The focusaltering device can converge or diverge the lens. The focus alteringdevice may alter the focus (e.g., before, after, and/or during the 3Dprinting) dynamically. The dynamic focus alteration may result in arange of focus alteration of the energy beam. The focus altering devicemay be static or dynamic. The dynamic focus altering device may becontroller (e.g., manually and/or automatically by a controller). Thedynamic focus alteration may be motorized (e.g., using at least onemotor).

In some embodiments, the controller controls the level of pressure(e.g., vacuum, ambient, or positive pressure) in the material removalmechanism material dispensing mechanism, and/or the enclosure (e.g.,chamber). The pressure level (e.g., vacuum, ambient, or positivepressure) may be constant or varied. The pressure level may be turned onand off manually and/or automatically (e.g., by the controller). Thecontroller may control at least one characteristic and/or component ofthe layer dispensing mechanism. For example, the controller may controlthe direction and/or rate of movement of the layer dispensing mechanismand any of its components, with respect to the target surface. Thecontroller may control the cooling member (e.g., external and/orinternal). The movement of the layer dispensing mechanism or any of itscomponents may be predetermined. The movement of the layer dispensingmechanism or any of its components may be according to an algorithm.Other control examples can be found in patent applications No.62/265,817, or patent application number PCT/US15/36802, both of whichare incorporated herein by reference in their entirety. The control maybe manual and/or automatic. The control may be programmed and/or beeffectuated a whim. The control may be according to an algorithm. Thealgorithm may comprise a 3D printing algorithm, or a motion controlalgorithm. The algorithm may take into account the (virtual) model ofthe 3D object.

In some embodiments, the controller comprises a processing unit. Theprocessing unit may be central. The processing unit may comprise acentral processing unit (herein “CPU”). The controllers or controlmechanisms (e.g., comprising a computer system) may be programmed toimplement methods of the disclosure. The controller may control at leastone component of the systems and/or apparatuses disclosed herein. FIG.11 is a schematic example of a computer system 1100 that is programmedor otherwise configured to facilitate the formation of a 3D objectaccording to the methods provided herein. The computer system 1100 cancontrol (e.g., direct and/or regulate) various features of printingmethods, software, apparatuses and systems of the present disclosure,such as, for example, regulating force, translation, heating, coolingand/or maintaining the temperature of a material bed (e.g., powder bed),process parameters (e.g., chamber pressure), scanning rate (e.g., of theenergy beam and/or the platform), scanning route of the energy source,position and/or temperature of the cooling member(s), application of theamount of energy emitted to a selected location, or any combinationthereof The computer system 1101 can be part of, or be in communicationwith, a printing system or apparatus, such as a 3D printing system orapparatus of the present disclosure. The computer may be operativelycoupled to one or more mechanisms disclosed herein, and/or any partsthereof. For example, the computer may be operatively coupled to one ormore sensors, valves, switches, motors, pumps, optical components, orany combination thereof.

In some embodiments, the computer system 1100 includes a processing unit1106 (also “processor,” “computer” and “computer processor” usedherein). The computer system may include memory or memory location 1102(e.g., random-access memory, read-only memory, flash memory), electronicstorage unit 1104 (e.g., hard disk), communication interface 1103 (e.g.,network adapter) for communicating with one or more other systems, andperipheral devices 1105, such as cache, other memory, data storageand/or electronic display adapters. The memory 1102, storage unit 1104,interface 1103, and peripheral devices 1105 are in communication withthe processing unit 1106 through a communication bus (solid lines), suchas a motherboard. The storage unit can be a data storage unit (or datarepository) for storing data. The computer system can be operativelycoupled to a computer network (“network”) 1101 with the aid of thecommunication interface. The network can be the Internet, and/or aninternet and/or extranet (e.g., an intranet and/or extranet that is incommunication with the Internet). In some cases, the network is atelecommunication and/or data network. The network can include one ormore computer servers, which can enable distributed computing, such ascloud computing. The network, in some cases with the aid of the computersystem, can implement a peer-to-peer network, which may enable devicescoupled to the computer system to behave as a client or a server.

In some embodiments, the processing unit executes a sequence ofmachine-readable instructions that can be embodied in a program orsoftware. The instructions may be stored in a memory location, such asthe memory 1102. The instructions can be directed to the processingunit, which can subsequently program or otherwise configure theprocessing unit to implement methods of the present disclosure. Examplesof operations performed by the processing unit can include fetch,decode, execute, and/or write back. The processing unit may interpretand/or execute instructions. The processor may include a microprocessor,a data processor, a central processing unit (CPU), a graphicalprocessing unit (GPU), a system-on-chip (SOC), a co-processor, a networkprocessor, an application specific integrated circuit (ASIC), anapplication specific instruction-set processor (ASIPs), a controller, aprogrammable logic device (PLD), a chipset, a field programmable gatearray (FPGA), or any combination thereof The processing unit can be partof a circuit, such as an integrated circuit. One or more othercomponents of the system 1100 can be included in the circuit.

In some embodiments, the storage unit (e.g., 1104) stores files, such asdrivers, libraries and/or saved programs. The storage unit can storeuser data (e.g., user preferences and user programs). In some cases, thecomputer system can include one or more additional data storage unitsthat are external to the computer system, such as located on a remoteserver that is in communication with the computer system through anintranet or the Internet.

In some embodiments, the computer system communicates with one or moreremote computer systems through the network. For instance, the computersystem can communicate with a remote computer system of a user (e.g.,operator). Examples of remote computer systems include personalcomputers (e.g., portable PC), slate or tablet PC's (e.g., Apple® iPad,Samsung® Galaxy Tab), telephones, Smart phones (e.g., Apple® iPhone,Android-enabled device, Blackberry®), or personal digital assistants.The user can access the computer system via the network.

In some embodiments, the methods described herein are implemented by wayof machine (e.g., computer processor) executable code stored on anelectronic storage location of the computer system, such as, forexample, on the memory (e.g., 1102) or electronic storage unit (e.g.,1104). The machine executable or machine-readable code can be providedin the form of software. During use, the processor (e.g., 1106) canexecute the code. In some cases, the code can be retrieved from thestorage unit and stored on the memory for ready access by the processor.In some situations, the electronic storage unit can be precluded, andmachine-executable instructions are stored on memory. The code can bepre-compiled and configured for use with a machine comprising aprocesser adapted to execute the code, or can be compiled duringruntime. The code can be supplied in a programming language that can beselected to enable the code to execute in a pre-compiled or as-compiledfashion.

In some embodiments, the processing unit includes one or more cores. Thecomputer system may comprise a single core processor, multi coreprocessor, or a plurality of processors for parallel processing. Theprocessing unit may comprise one or more central processing unit (CPU)and/or a graphic processing unit (GPU). The multiple cores may bedisposed in a physical unit (e.g., Central Processing Unit, or GraphicProcessing Unit). The processing unit may include one or more processingunits. The physical unit may be a single physical unit. The physicalunit may be a die. The physical unit may comprise cache coherencycircuitry. The multiple cores may be disposed in close proximity. Thephysical unit may comprise an integrated circuit chip. The integratedcircuit chip may comprise one or more transistors. The integratedcircuit chip may comprise at least about 0.2 billion transistors (BT),0.5 BT, 1 BT, 2 BT, 3 BT, 5 BT, 6 BT, 7 BT, 8 BT, 9 BT, 10 BT, 15 BT, 20BT, 25 BT, 30 BT, 40 BT, or 50 BT. The integrated circuit chip maycomprise at most about 7 BT, 8 BT, 9 BT, 10 BT, 15 BT, 20 BT, 25 BT, 30BT, 40 BT, 50 BT, 70 BT, or 100 BT. The integrated circuit chip maycomprise any number of transistors between the afore-mentioned numbers(e.g., from about 0.2 BT to about 100 BT, from about 1 BT to about 8 BT,from about 8 BT to about 40 BT, or from about 40 BT to about 100 BT).The integrated circuit chip may have an area of at least about 50 mm²,60 mm², 70 mm², 80 mm², 90 mm², 100 mm², 200 mm², 300 mm², 400 mm², 500mm², 600 mm², 700 mm², or 800 mm². The integrated circuit chip may havean area of at most about 50 mm², 60 mm², 70 mm², 80 mm², 90 mm², 100mm², 200 mm², 300 mm², 400 mm², 500 mm², 600 mm², 700 mm², or 800 mm².The integrated circuit chip may have an area of any value between theafore-mentioned values (e.g., from about 50 mm² to about 800 mm², fromabout 50 mm² to about 500 mm², or from about 500 mm² to about 800 mm²).The close proximity may allow substantial preservation of communicationsignals that travel between the cores. The close proximity may diminishcommunication signal degradation. A core, as understood herein, is acomputing component having independent central processing capabilities.The computing system may comprise a multiplicity of cores, which aredisposed on a single computing component. The multiplicity of cores mayinclude two or more independent central processing units. Theindependent central processing units may constitute a unit that readsand executes program instructions. The independent central processingunits may constitute one or more parallel processing units. The parallelprocessing units may be cores and/or digital signal processing slices(DSP slices). The multiplicity of cores can be parallel cores. Themultiplicity of DSP slices can be parallel DSP slices. The multiplicityof cores and/or DSP slices can function in parallel. The multiplicity ofcores may include at least about 2, 10, 40, 100, 400, 1000, 2000, 3000,4000, 5000, 6000, 7000, 8000, 9000, 10000, 11000, 12000, 13000, 14000 or15000 cores. The multiplicity of cores may include at most about 1000,2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000, 11000, 12000,13000, 14000, 15000, 20000, 30000, or 40000 cores. The multiplicity ofcores may include cores of any number between the afore-mentionednumbers (e.g., from about 2 to about 40000, from about 2 to about 400,from about 400 to about 4000, from about 2000 to about 4000, from about4000 to about 10000, from about 4000 to about 15000, or from about 15000to about 40000 cores). In some processors (e.g., FPGA), the cores may beequivalent to multiple digital signal processor (DSP) slices (e.g.,slices). The plurality of DSP slices may be equal to any of pluralitycore values mentioned herein. The processor may comprise low latency indata transfer (e.g., from one core to another). Latency may refer to thetime delay between the cause and the effect of a physical change in theprocessor (e.g., a signal). Latency may refer to the time elapsed fromthe source (e.g., first core) sending a packet to the destination (e.g.,second core) receiving it (also referred as two-point latency).One-point latency may refer to the time elapsed from the source (e.g.,first core) sending a packet (e.g., signal) to the destination (e.g.,second core) receiving it, and the destination sending a packet back tothe source (e.g., the packet making a round trip). The latency may besufficiently low to allow a high number of floating point operations persecond (FLOPS). The number of FLOPS may be at least about 0.1 Tera FLOPS(T-FLOPS), 0.2 T-FLOPS, 0.25 T-FLOPS, 0.5 T-FLOPS, 0.75 T-FLOPS, 1T-FLOPS, 2 T-FLOPS, 3 T-FLOPS, 5 T-FLOPS, 6 T-FLOPS, 7 T-FLOPS, 8T-FLOPS, 9 T-FLOPS, or 10 T-FLOPS. The number of flops may be at mostabout 0.2 T-FLOPS, 0.25 T-FLOPS, 0.5 T-FLOPS, 0.75 T-FLOPS, 1 T-FLOPS, 2T-FLOPS, 3 T-FLOPS, 5 T-FLOPS, 6 T-FLOPS, 7 T-FLOPS, 8 T-FLOPS, 9T-FLOPS, 10 T-FLOPS, 20 T-FLOPS, 30 T-FLOPS, 50 T-FLOPS, 100 T-FLOPS, 1P-FLOPS, 2 P-FLOPS, 3 P-FLOPS, 4 P-FLOPS, 5 P-FLOPS, 10 P-FLOPS, 50P-FLOPS, 100 P-FLOPS, 1 EXA-FLOP, 2 EXA-FLOPS or 10 EXA-FLOPS. Thenumber of FLOPS may be any value between the afore-mentioned values(e.g., from about 0.1 T-FLOP to about 10 EXA-FLOPS, from about 0.1T-FLOPS to about 1 T-FLOPS, from about 1 T-FLOPS to about 4 T-FLOPS,from about 4 T-FLOPS to about 10 T-FLOPS, from about 1 T-FLOPS to about10 T-FLOPS, from about 10 T-FLOPS to about 30 T-FLOPS, from about 50T-FLOPS to about 1 EXA-FLOP, or from about 0.1 T-FLOP to about 10EXA-FLOPS). In some processors (e.g., FPGA), the operations per secondmay be measured as (e.g., Giga) multiply-accumulate operations persecond (e.g., MACs or GMACs). The MACs value can be equal to any of theT-FLOPS values mentioned herein measured as Tera-MACs (T-MACs) insteadof T-FLOPS respectively. The FLOPS can be measured according to abenchmark. The benchmark may be a HPC Challenge Benchmark. The benchmarkmay comprise mathematical operations (e.g., equation calculation such aslinear equations), graphical operations (e.g., rendering), orencryption/decryption benchmark. The benchmark may comprise a HighPerformance UNPACK, matrix multiplication (e.g., DGEMM), sustainedmemory bandwidth to/from memory (e.g., STREAM), array transposing ratemeasurement (e.g., PTRANS), Random-access, rate of Fast FourierTransform (e.g., on a large one-dimensional vector using the generalizedCooley-Tukey algorithm), or Communication Bandwidth and Latency (e.g.,MPI-centric performance measurements based on the effectivebandwidth/latency benchmark). UNPACK may refer to a software library forperforming numerical linear algebra on a digital computer. DGEMM mayrefer to double precision general matrix multiplication. STREAMbenchmark may refer to a synthetic benchmark designed to measuresustainable memory bandwidth (in MB/s) and a corresponding computationrate for four simple vector kernels (Copy, Scale, Add and Triad). PTRANSbenchmark may refer to a rate measurement at which the system cantranspose a large array (global). MPI may refer to Message PassingInterface.

The computer system may include hyper-threading technology. The computersystem may include a chip processor with integrated transform, lighting,triangle setup, triangle clipping, rendering engine, or any combinationthereof The rendering engines may be capable of processing at leastabout 10 million calculations per second. The rendering engine may becapable of processing at least about 10 million polygons per second. Asan example, the GPU may include a GPU by Nvidia, ATI Technologies, S3Graphics, Advanced Micro Devices (AMD), or Matrox. The processing unitmay be able to process algorithms comprising a matrix or a vector. Thecore may comprise a complex instruction set computing core (CISC), orreduced instruction set computing (RISC).

In some examples, the computer system includes an electronic chip thatis reprogrammable (e.g., field programmable gate array (FPGA)). Forexample, the FPGA may comprise Tabula, Altera, or Xilinx FPGA. Theelectronic chips may comprise one or more programmable logic blocks(e.g., an array). The logic blocks may compute combinational functions,logic gates, or any combination thereof The computer system may includecustom hardware. The custom hardware may comprise an algorithm.

In some embodiments, the computer system includes configurablecomputing, partially reconfigurable computing, reconfigurable computing,or any combination thereof The computer system may include an FPGA. Thecomputer system may include an integrated circuit that performs thealgorithm. For example, the reconfigurable computing system may compriseFPGA, CPU, GPU, or multi-core microprocessors. The reconfigurablecomputing system may comprise a High-Performance ReconfigurableComputing architecture (HPRC). The partially reconfigurable computingmay include module-based partial reconfiguration, or difference-basedpartial reconfiguration. The reconfigurable computing environment maycomprise reconfigure one or more models (e.g., physical models) used for3D printing. The FPGA may comprise configurable FPGA logic, and/orfixed-function hardware comprising: multipliers, memories,microprocessor cores, first in-first out (FIFO) and/or error correctingcode (ECC) logic, digital signal processing (DSP) blocks, peripheralcomponent interconnect express (PCI Express) controllers, Ethernet mediaaccess control (MAC) blocks, or high-speed serial transceivers. DSPblocks can be DSP slices.

In some embodiments, the computing system includes an integrated circuitthat performs the algorithm (e.g., control algorithm). The physical unit(e.g., the cache coherency circuitry within) may have a clock time of atleast about 0.1 Gigabits per second (Gbit/s), 0.5 Gbit/s, 1 Gbit/s, 2Gbit/s, 5 Gbit/s, 6 Gbit/s, 7 Gbit/s, 8 Gbit/s, 9 Gbit/s, 10 Gbit/s, or50 Gbit/s. The physical unit may have a clock time of any value betweenthe afore-mentioned values (e.g., from about 0.1 Gbit/s to about 50Gbit/s, or from about 5 Gbit/s to about 10 Gbit/s). The physical unitmay produce the algorithm output in at most about 0.1 microsecond (μs),1 μs, 10 μs, 100 μs, or 1 millisecond (ms). The physical unit mayproduce the algorithm output in any time between the afore-mentionedtimes (e.g., from about 0.1 μs, to about 1 ms, from about 0.1 μs, toabout 100 μs, or from about 0.1 μs to about 10 μs).

In some instances, the controller uses calculations, real timemeasurements, or any combination thereof, to regulate at least onecharacteristic of the energy beam(s) and/or energy source(s). The sensor(e.g., temperature and/or metrological sensor) may provide a signal(e.g., input for the controller and/or processor) at a rate of at leastabout 0.1 KHz, 1 KHz, 10 KHz, 100 KHz, 1000 KHz, or 10000 KHz). Thesensor may provide a signal at a rate between any of the above-mentionedrates (e.g., from about 0.1 KHz to about 10000 KHz, from about 0.1 KHzto about 1000 KHz, or from about 1000 KHz to about 10000 KHz). Thememory bandwidth of the processing unit may be at least about 1gigabytes per second (Gbytes/s), 10 Gbytes/s, 100 Gbytes/s, 200Gbytes/s, 300 Gbytes/s, 400 Gbytes/s, 500 Gbytes/s, 600 Gbytes/s, 700Gbytes/s, 800 Gbytes/s, 900 Gbytes/s, or 1000 Gbytes/s. The memorybandwidth of the processing unit may be at most about 1 gigabyte persecond (Gbytes/s), 10 Gbytes/s, 100 Gbytes/s, 200 Gbytes/s, 300Gbytes/s, 400 Gbytes/s, 500 Gbytes/s, 600 Gbytes/s, 700 Gbytes/s, 800Gbytes/s, 900 Gbytes/s, or 1000 Gbytes/s. The memory bandwidth of theprocessing unit may have any value between the afore-mentioned values(e.g., from about 1 Gbytes/s to about 1000 Gbytes/s, from about 100Gbytes/s to about 500 Gbytes/s, from about 500 Gbytes/s to about 1000Gbytes/s, or from about 200 Gbytes/s to about 400 Gbytes/s). The sensormeasurements may be real-time measurements. The real time measurementsmay be conducted during the 3D printing process. The real-timemeasurements may be in situ measurements in the 3D printing systemand/or apparatus. the real time measurements may be during at least aportion of the formation of the 3D object. In some instances, theprocessing unit may use the signal obtained from the at least one sensorto provide a processing unit output, which output is provided by theprocessing system at a speed of at most about 100 min, 50 min, 25 min,15 min, 10 min, 5 min, 1 min, 0.5 min (i.e., 30 sec), 15 sec, 10 sec, 5sec, 1 sec, 0.5 sec, 0.25 sec, 0.2 sec, 0.1 sec, 80 milliseconds (msec),50 msec, 10 msec, 5 msec, 1 msec, 80 microseconds (μsec), 50 μsec, 20μsec, 10 μsec, 5 μsec, or 1 μsec. In some instances, the processing unitmay use the signal obtained from the at least one sensor to provide aprocessing unit output, which output is provided at a speed of any valuebetween the afore-mentioned values (e.g., from about 100 min to about 1μsec, from about 100 min to about 10 min, from about 10 min to about 1min, from about 5 min to about 0.5 min, from about 30 sec to about 0.1sec, from about 0.1 sec to about 1 msec, from about 80 msec to about 10μsec, from about 50 μsec to about 1 μsec, from about 20 μsec to about 1μsec, or from about 10 μsec to about 1 μsec).

The processing unit output may comprise an evaluation of: a temperatureat a location, a map of temperatures at locations, a position at alocation (e.g., vertical and/or horizontal), or a map of positions atlocations. The position may be horizontal and/or vertical. The positionmay be in space (e.g., comprising X Y and Z coordinates). The locationmay be on the target surface. The map may comprise a topological and/ortemperature map. The temperature sensor may comprise a temperatureimaging device (e.g., IR imaging device).

In some embodiments, the processing unit uses the signal obtained fromthe at least one sensor in an algorithm that is used in controlling theenergy beam (e.g., in the 3D printing instructions). The algorithm maycomprise the path of the energy beam. In some instances, the algorithmmay be used to alter the path (e.g., trajectory) of the energy beam onthe target surface. The path may deviate from a cross section of a(virtual) model corresponding to the desired 3D object. The processingunit may use the output in an algorithm that is used in determining themanner in which a model of the desired 3D object may be sliced. In someembodiments, the processing unit uses the signal obtained from the atleast one sensor in an algorithm that is used to configure one or moreparameters, systems, and/or apparatuses relating to the 3D printingprocess. The parameters may comprise a characteristic of the energybeam. The parameters may comprise movement of the platform and/ormaterial bed. The parameters may comprise relative movement of theenergy beam to the material bed. In some instances, the energy beam, theplatform (e.g., material bed disposed on the platform), or both maytranslate. Alternatively or additionally, the controller may usehistorical data for the control. Alternatively or additionally, theprocessing unit may use historical data in its one or more algorithms.The parameters may comprise the height of the layer of pre-transformed(e.g., powder) material disposed in the enclosure and/or the gap bywhich the cooling element (e.g., heat sink) is separated from the targetsurface. The target surface may be the exposed layer of the materialbed.

In some embodiments, aspects of the systems, apparatuses, and/or methodsprovided herein, such as the computer system, are embodied inprogramming (e.g., using a software). Various aspects of the technologymay be thought of as “product,” “object,” or “articles of manufacture”typically in the form of machine (or processor) executable code and/orassociated data that is carried on or embodied in a type ofmachine-readable medium. Machine-executable code can be stored on anelectronic storage unit, such as memory (e.g., read-only memory,random-access memory, flash memory) or a hard disk. The storage maycomprise non-volatile storage media. “Storage” type media can includeany or all the tangible memory of the computers, processors or the like,or associated modules thereof, such as various semiconductor memories,tape drives, disk drives, external drives, and the like, which mayprovide non-transitory storage at any time for the software programming.The memory may comprise a random-access memory (RAM), dynamic randomaccess memory (DRAM), static random access memory (SRAM), synchronousdynamic random access memory (SDRAM), ferroelectric random access memory(FRAM), read only memory (ROM), programmable read only memory (PROM),erasable programmable read only memory (EPROM), electrically erasableprogrammable read only memory (EEPROM), a flash memory, or anycombination thereof The flash memory may comprise a negative-AND (NAND)or NOR logic gates. A NAND gate (negative-AND) may be a logic gate whichproduces an output which is false only if all its inputs are true. Theoutput of the NAND gate may be complement to that of the AND gate. Thestorage may include a hard disk (e.g., a magnetic disk, an optical disk,a magneto-optic disk, a solid-state disk, etc.), a compact disc (CD), adigital versatile disc (DVD), a floppy disk, a cartridge, a magnetictape, and/or another type of computer-readable medium, along with acorresponding drive.

In some embodiments, at least portions (e.g., all) of the software mayat times be communicated through the Internet or various othertelecommunication networks. Such communications, for example, may enableloading of the software from one computer or processor into another, forexample, from a management server and/or a host computer, into thecomputer platform of an application server. Thus, another type of mediathat may bear the software elements comprises optical, electrical, orelectromagnetic waves; for example, such as the ones used acrossphysical interfaces between local devices, through wired and opticallandline networks, and/or over various air-links. The physical elementsthat carry such waves (e.g., such as wired or wireless links, opticallinks, or the like) also may be considered as media bearing thesoftware. As used herein, unless restricted to non-transitory, tangible“storage” media, terms such as computer or machine “readable medium”refer to any medium that participates in providing instructions to aprocessor for execution. Hence, a machine-readable medium, such ascomputer-executable code, may take many forms, including but not limitedto, a tangible storage medium, a carrier wave medium, or physicaltransmission medium. Non-volatile storage media include, for example,optical or magnetic disks, such as any of the storage devices in anycomputer(s) or the like, such as may be used to implement the databases.Volatile storage media can include dynamic memory, such as main memoryof a computer platform. Tangible transmission media can include coaxialcables, wire (e.g., copper wire), and/or fiber optics, including thewires that comprise a bus within a computer system. Carrier-wavetransmission media may take the form of electric or electromagneticsignals, or acoustic or light waves such as those generated during radiofrequency (RF) and infrared (IR) data communications. Common forms ofcomputer-readable media therefore include for example: a floppy disk, aflexible disk, hard disk, magnetic tape, any other magnetic medium, aCD-ROM, DVD or DVD-ROM, any other optical medium, punch cards papertape, any other physical storage medium with patterns of holes, a RAM, aROM, a PROM and EPROM, a FLASH-EPROM, any other memory chip orcartridge, a carrier wave transporting data or instructions, cables orlinks transporting such a carrier wave, any other medium from which acomputer may read programming code and/or data, or any combinationthereof. The memory and/or storage may comprise a storing deviceexternal to and/or removable from device, such as a Universal Serial Bus(USB) memory stick, or/and a hard disk. Many of these forms of computerreadable media may be involved in carrying one or more sequences of oneor more instructions to a processor for execution.

In some embodiments, the computer system includes and/or is incommunication with an electronic display. The electronic display maycomprise a user interface (UI) for providing, for example, a modeldesign or graphical representation of a 3D object to be printed (e.g.,before, after, and/or during the 3D printing (e.g. in real-time)).Examples of UI's include, without limitation, a graphical user interface(GUI) and web-based user interface. The computer system can monitorand/or control various aspects of the 3D printing system. The controlmay be manual and/or programmed. The control may rely on one or morefeedback mechanisms (e.g., using signals from the one or more sensors).The control may consider historical data. The control mechanism may bepre-programmed. The control mechanisms may rely on input from sensors(described herein) that are connected to the control unit (i.e., controlsystem or control mechanism). The computer system may store historicaldata concerning various aspects of the operation of the 3D printer. Thehistorical data may be retrieved at predetermined times and/or at awhim. The historical data may be accessed by an operator and/or by auser. The historical, sensor, and/or operative data may be provided inan output unit (e.g., a display unit). The output unit (e.g., monitor)may output various parameters of the 3D printing system (as describedherein) in real time and/or in a delayed time (e.g., before, after,and/or during the 3D printing). The output unit may output the current3D printed object (e.g., build), the requested (e.g., ordered) 3Dprinted object, or both. The output unit may output the printingprogress of the 3D printed object (e.g., in rea-time). The output unitmay output at least one of the total time, time remaining, and timeexpanded on printing the 3D object. The output unit may output (e.g.,display, voice, and/or print) the status of sensors, their reading,and/or time for their calibration or maintenance. The output unit mayoutput the type of material(s) used and various characteristics of thematerial(s) such as temperature and flowability of the pre-transformedmaterial. The output unit may output the amount of oxygen, water, andpressure in the printing chamber (i.e., the chamber where the 3D objectis being printed). The computer may generate a report comprising variousparameters of the 3D printing system, method, and or objects atpredetermined time(s), on a request (e.g., from an operator), and/or ata whim. The output unit may comprise a screen, printer, or speaker. Thecontrol system may provide a report. The report may comprise any itemsrecited as an output of the output unit.

In some embodiments, the system and/or apparatus described herein (e.g.,controller) and/or any of their components comprise an output and/or aninput device. The input device may comprise a keyboard, touch pad, ormicrophone. The output device may be a sensory output device. The outputdevice may comprise a visual, tactile, or audio device. The audio devicemay include a loudspeaker. The visual output device may include a screenand/or a printed hard copy (e.g., paper). The output device may includea (e.g., two-dimensional) printer (e.g., paper printer). The apparatusmay record one or more operations and/or specifications of the systemand/or apparatus. The record may be used for process optimization,certification, and/or specification. The input device may include acamera, a microphone, a keyboard, or a (e.g., touch) screen. The systemand/or apparatus described herein (e.g., controller) and/or any of theircomponents may comprise Bluetooth technology. The system and/orapparatus described herein (e.g., controller) and/or any of theircomponents may comprise a communication port. The communication port maybe a serial port or a parallel port. The communication port may be aUniversal Serial Bus port (i.e., USB). The system and/or apparatusdescribed herein (e.g., controller) and/or any of their components maycomprise USB ports. The USB can be micro or mini USB. The USB port mayrelate to device classes comprising 00h, 01h, 02h, 03h, 05h, 06h, 07h,08h, 09h, 0Ah, 0Bh, 0Dh, 0Eh, 0Fh, 10h, 11h, DCh, E0h, EFh, FEh, or FFh.The system and/or apparatus described herein (e.g., controller) and/orany of their components may comprise a plug and/or a socket (e.g.,electrical, AC power, DC power). The system and/or apparatus describedherein (e.g., controller) and/or any of their components may comprise anadapter (e.g., AC and/or DC power adapter). The system and/or apparatusdescribed herein (e.g., controller) and/or any of their components maycomprise a power connector. The power connector can be an electricalpower connector. The power connector may comprise a magnetically coupled(e.g., attached) power connector. The power connector can be a dockconnector. The connector can be a data and power connector. Theconnector may comprise pins. The connector may comprise at least 10, 15,18, 20, 22, 24, 26, 28, 30, 40, 42, 45, 50, 55, 80, or 100 pins.

In some examples, the systems, methods, software, and/or apparatusesdisclosed herein may comprise receiving a request for a 3D object (e.g.,from a customer). The request can include a model (e.g., CAD) of thedesired 3D object. Alternatively or additionally, a (virtual) model ofthe desired 3D object may be generated. The model may be used togenerate 3D printing instructions. In some examples, the 3D printinginstructions may exclude the 3D model (e.g., and include a modificationthereof, e.g., a geometric modification). The 3D printing instructionsmay be based on the 3D model. The 3D printing instructions may take the3D model into account. The 3D printing instructions may be alternativelyor additionally based on simulations (e.g., thermos-mechanicalsimulations). The 3D printing instructions may use the 3D model. The 3Dprinting instructions may comprise using an algorithm (e.g., embedded ina software) that takes into account the 3D model, simulations,historical data, sensor input, or any combination thereof The controlcan be of at least one characteristic of the energy beam (e.g., asdisclosed herein). The control can comprise using a simulation. Thecomputer model (e.g., physical model) may comprise one or moresimulation. The simulation can comprise a temperature or mechanicalsimulation of the 3D printing (e.g., of the desired and/or requested 3Dobject). The simulation may comprise thermo-mechanical simulation. Thesimulation can comprise a material property of the requested 3D object.The thermo-mechanical simulation can comprise elastic or plasticsimulation. The control can comprise using a graphical processing unit(GPU), system-on-chip (SOC), application specific integrated circuit(ASIC), application specific instruction-set processor (ASIPs),programmable logic device (PLD), or field programmable gate array(FPGA). The processor may compute at least a portion of the algorithmduring the 3D printing process (e.g., in real-time), during theformation of the 3D object, prior to the 3D printing process, after the3D printing process, or any combination thereof The processor maycompute the algorithm in the interval between pulses of the (e.g.,transforming) energy beam, during the dwell time of the energy beam,before the energy beam translates to a new position, while the energybeam is not translating, while the energy beam does not irradiate thetarget surface, while the energy beam irradiates the target surface, orany combination thereof. For example, the processor may compute thealgorithm while the energy beam translates and does substantially notirradiate the exposed surface. For example, the processor may computethe algorithm while the energy beam does not translate and/or irradiatesthe exposed surface. For example, the processor may compute thealgorithm while the energy beam does not substantially translate anddoes substantially not irradiate the exposed surface. For example, theprocessor may compute the algorithm while the energy beam does translateand/or irradiates the exposed surface. The translation of the energybeam may be translation along an entire path or a portion thereof Thepath may correspond to a cross section of the model of the requested 3Dobject. The translation of the energy beam may be translation along atleast one hatching within the path. FIG. 13 shows examples of variouspaths. The direction of the arrow(s) in FIG. 13 represents the directionaccording to which the energy beam scans the target surface. The pathmay correspond to a positon in the exposed surface of the material bedwith which the energy beam interacts. The various vectors depicted inFIG. 13, 1314 show an example of various hatchings. The respectivemovement of the energy beam with respect to the material bed mayoscillate while traveling along the path. For example, the propagationof the energy beam along a path may be by small path deviations (e.g.,variations such as oscillations). FIG. 12 shows an example of a path1201. The sub path 1202 is a magnification of a portion of the path 1201showing path deviations (e.g., oscillations).

EXAMPLES

The following are illustrative and non-limiting examples of methods ofthe present disclosure.

Example 1

In a 25 cm by 25 cm by 30 cm container at ambient temperature andpressure, Inconel 718 powder of average particle size 32 μm is depositedto form a powder bed. A 200 W 1060 nm fiber-laser beam fabricated aplurality of rectangular 3D objects comprising elongated surfaces ofapproximate dimensions 6 mm by 30 mm, 3D objects were formed by meltingrespective portions of the powder bed. The fabricated 3D objects wereanchorlessly suspended in the powder bed during and after theirfabrication. The surfaces expressed various degrees of warping asdepicted in FIG. 19 (e.g., 1903, 1904, and 1905). A visible lightemitting diode projected a sine wave on the exposed surface of thepowder bed containing these surfaces, visibly showing their planarity orthe degree of deviation from planarity of various portions of thesurfaces. The deviation may be correlated to the manner (e.g., magnitudeand direction) of deviation from the expected projection of theoscillating light (e.g., 1901 and 1902) or lack thereof. The portion ofthe powder bed containing the surfaces was imaged by a 4 Mega pixelcomplementary metal-oxide-semiconductor (CMOS) camera. The sine waveimage on the camera has a periodicity of approximately 16 pixels.

Example 2

In a processing chamber at ambient atmosphere and temperature, and at apressure of about 3,000 Pa above atmospheric pressure, a planar 3Dobject made of Inconel 718 was disposed above a base, which planar 3Dobject was 6 mm wide, 25 mm long, and 770 micrometers thick. A 400 Wfiber 1060 nm laser beam fabricated a series of tiles as follows: (a) aplanar exposed surface of the 3D object was irradiated with a defocusedGaussian beam of cross section diameter of about 0.5 mm (measured at1/e² of the Gaussian beam) during dwell time t₁, to form a first tile(e.g., FIG. 35, 3501); (b) the laser beam translated to the position ofthe future second tile during intermission time t₂; and (c) the energybeam irradiated at the second position during dwell time t₃ to form thesecond tile (e.g., FIG. 35, 3502). Steps (a)-(c) were repeated while theenergy beam moved along a predetermined trajectory with predetermineddwell time scheme (e.g., using open loop control) to form the tiledsurface shown in FIG. 35 as a top view that depicts a series ofsubstantially identical tiles. The delay time t2 was substantiallyconstant during the formation of the tiled surface. The dwell times(e.g., t1 and t3) were varied to predetermined times to form melt poolsof substantially constant dimensions. This was done while overcoming thepre-heating effect of previously formed melt pools, as well as edgeeffects at the edge of the melt pool array. The 3D object was notanchored to the base during irradiation of the laser. The power of thelaser stayed substantially constant during its irradiation. FIG. 35 wasimaged by a 2 Mega pixel charge-coupled device (CCD) camera under anoptical microscope.

While preferred embodiments of the present invention have been shown anddescribed herein, it will be obvious to those skilled in the art thatsuch embodiments are provided by way of example only. It is not intendedthat the invention be limited by the specific examples provided withinthe specification. While the invention has been described with referenceto the aforementioned specification, the descriptions and illustrationsof the embodiments herein are not meant to be construed in a limitingsense. Numerous variations, changes, and substitutions will now occur tothose skilled in the art without departing from the invention.Furthermore, it shall be understood that all aspects of the inventionare not limited to the specific depictions, configurations, or relativeproportions set forth herein which depend upon a variety of conditionsand variables. It should be understood that various alternatives to theembodiments of the invention described herein may be employed inpracticing the invention. It is therefore contemplated that theinvention shall also cover any such alternatives, modifications,variations, or equivalents. It is intended that the following claimsdefine the scope of the invention and that methods and structures withinthe scope of these claims and their equivalents be covered thereby.

What is claimed is:
 1. A method for three-dimensional printing analysis,comprising: (a) using at least one processor to execute a simulation ofan electrical circuit model to produce a result, which electricalcircuit model comprises one or more electrical component that analogizea heat capacity and/or a thermal conductivity of a material type used inthe three-dimensional printing to print at least one three-dimensionalobject that includes one or more layers, which simulation evaluates atemperature distribution of the at least one three-dimensional object;and (b) using the at least one processor to output the result.
 2. Themethod of claim 1, wherein the simulation occurs during a time at whicha layer of one or more layers is printed by the three-dimensionalprinting.
 3. The method of claim 1, wherein using the at least oneprocessor to output the result comprises storing the result in acomputer memory device.
 4. The method of claim 1, wherein the result isconfigured for utilization in printing the at least onethree-dimensional objects.
 5. The method of claim 1, wherein theelectrical circuit model comprises an electrical component, whichelectrical component comprises a passive or an electromechanicalcomponent.
 6. The method of claim 1, wherein the electrical circuitmodel comprises an electronic component, which electrical componentcomprises a variable component.
 7. The method of claim 1, wherein thesimulation comprises using the electrical circuit model to imitate oneor more the physical properties of the three-dimensional printing byusing electrical circuit model.
 8. The method of claim 1, wherein theelectrical circuit model comprises a resistor, capacitor, groundelement, current source, voltage element, or an electrical branch. 9.The method of claim 8, wherein the electrical branch comprises aresistor coupled in parallel to a capacitor.
 10. The method of claim 8,wherein the electrical branch represents one or more physical propertiesrelated to printing the at least one three-dimensional object.
 11. Themethod of claim 10, wherein the one or more physical propertiescomprises a (i) heat profile, (ii) thermal history, (iii) power profileof an energy source utilized in the three-dimensional printing, or (iv)irradiation profile of an energy beam utilized in the three-dimensionalprinting.
 12. The method of claim 1, wherein the three-dimensionalprinting comprises transforming at least a portion of a pre-transformedmaterial using an energy beam.
 13. The method of claim 12, wherein thepre-transformed material is at least a portion of a material bed, andwherein the material bed is planarized using an apparatus comprising acyclonic separator.
 14. The method of claim 12, wherein thepre-transformed material comprises at least one member selected from thegroup consisting of an elemental metal, metal alloy, ceramic, and anallotrope of elemental carbon.
 15. A non-transitory computer-readablemedium in which program instructions are stored, which instructions,when read by a computer, cause the computer to perform operationscomprising: (a) executing a simulation of an evolution of a temperaturedistribution in at least one three-dimensional object that developsduring three-dimensional printing of the at least one three-dimensionalobject, to produce a result, which simulating is by using an electricalcircuit model that comprises one or more electrical components, whichone or more electrical components are analogous to a heat capacityand/or a thermal conductivity of a material type used in thethree-dimensional printing to print the at least one three-dimensionalobject; and (b) outputting the result of executing the simulation. 16.The non-transitory computer-readable medium of claim 15, whereinoutputting comprise storing the result in a computer memory device. 17.The non-transitory computer-readable medium of claim 15, wherein theresult is utilized to affect the three-dimensional printing of the atleast one three-dimensional object.
 18. The non-transitorycomputer-readable medium of claim 15, wherein the result is configuredto be utilized for predicting a deviation of the at least onethree-dimensional object from at least one requested three-dimensionalobject.
 19. The non-transitory computer-readable medium of claim 15,wherein the simulation occurs during a time at which a layer of one ormore layers is printed by the three-dimensional printing.
 20. Thenon-transitory computer-readable medium of claim 15, wherein theelectrical circuit model comprises an electrical component, whichelectrical component comprises a passive or an electromechanicalcomponent.
 21. The non-transitory computer-readable medium of claim 15,wherein the electrical circuit model comprises an electronic component,which electrical component comprises a variable component.
 22. Thenon-transitory computer-readable medium of claim 15, wherein thesimulation comprises using the electrical circuit model to imitate oneor more the physical properties of the three-dimensional printing byusing electrical circuit model.
 23. The non-transitory computer-readablemedium of claim 15, wherein the electrical circuit model comprises aresistor, capacitor, ground element, current source, voltage element, oran electrical branch.
 24. The non-transitory computer-readable medium ofclaim 23, wherein the electrical branch comprises a resistor coupled inparallel to a capacitor.
 25. The non-transitory computer-readable mediumof claim 23, wherein the electrical branch represents one or morephysical properties.
 26. The non-transitory computer-readable medium ofclaim 25, wherein the one or more physical properties comprises a (i)heat profile, (ii) thermal history, (iii) power profile of an energysource utilized in the three-dimensional printing, or (iv) irradiationprofile of an energy beam utilized in the three-dimensional printing.27. The non-transitory computer-readable medium of claim 23, wherein thethree-dimensional printing comprises transforming at least a portion ofa pre-transformed material using an energy beam.
 28. The non-transitorycomputer-readable medium of claim 27, wherein the pre-transformedmaterial comprises at least one member selected from the groupconsisting of an elemental metal, metal alloy, ceramic, and an allotropeof elemental carbon.